IntroductionThis package provides tools to generate plots and labeled axes easily. It draws normal plots, logplots and semi-logplots, in two and three dimensions. Axis ticks, labels, legends (in case of multiple plots) can be added with key-value options. It supports line plots, scatter plots, piecewise constant plots, bar plots, area plots, mesh and surface plots, patch plots, contour plots, quiver plots, histogram plots, box plots, polar axes, ternary diagrams, smith charts and some more. It can cycle through a set of predened line/marker/color specications. In summary, its purpose is to simplify the generation of high-quality function and/or data plots, and solving the problems of consistency of document and font type and font size, direct use of TEX math mode in axis descriptions, consistency of data and gures (no third party tool necessary), inter-document consistency using preamble congurations and styles.

Although not necessary, separate .pdf or .eps graphics can be generated using the external library developed as part of Tik Z. You are invited to use pgfplots for visualization of medium sized data sets in two and three dimensions. It is based on Till Tantaus package pgf/Tik Z.

Chapter 2

About pgfplots: Preliminaries

This section contains information about upgrades, the team, the installation (in case you need to do it manually) and troubleshooting. You may skip it completely except for the upgrade remarks. pgfplots is built completely on Tik Z/pgf. Knowledge of Tik Z will simplify the work with pgfplots, although it is not required. However, note that this library requires at least pgf version 2.10. At the time of this writing, many TEX-distributions still contain the older pgf version 1.18, so it may be necessary to install a recent pgf prior to using pgfplots.

2.1

Components

pgfplots comes with two components: 1. the plotting component (which you are currently reading) and 2. the PgfplotsTable component which simplies number formatting and postprocessing of numerical tables. It comes as a separate package and has its own manual pgfplotstable.pdf.

2.2

Upgrade remarks

This release provides a lot of improvements which can be found in all detail in ChangeLog for interested readers. However, some attention is useful with respect to the following changes.

2.2.1

New Optional Features

pgfplots has been written with backwards compatibility in mind: old TEX les should compile without modications and without changes in the appearance. However, new features occasionally lead to a dierent behavior. In such a case, pgfplots will deactivate the new feature1 . Any new features or bugxes which cause backwards compatibility problems need to be activated manually and explicitly. In order to do so, you should use\usepackage{pgfplots} \pgfplotsset{compat=1.9}

in your preamble. This will congure the compatibility layer. You should have at least compat=1.3. The suggested value is printed to the .log le after running TEX. Here is a list of changes introduced in recent versions of pgfplots: 1. pgfplots 1.9 comes with a preset to combine ybar stacked and nodes near coords. Furthermore, it suppresses empty increments in stacked bar plots. In order to activate the new preset, you have to use compat=1.9 or higher. 2. pgfplots 1.8 comes with a new revision for alignment of label- and tick scale label alignment. Furthermore, it improves the bounding box for hide axis. This revision is enabled with compat=1.8 or higher.1 In

case of broken backwards compatibility, we apologize and ask you to submit a bug report. We will take care of it.

2.2. UPGRADE REMARKS

The conguration compat=1.8 is nessecary to repair axis lines=center in threedimensional axes. 3. pgfplots 1.7 added new options for bar widths dened in terms of axis units. These are enabled with compat=1.7 or higher. 4. pgfplots 1.6 added new options for more accurate scaling and more scaling options for \addplot3 graphics. These are enabled with compat=1.6 or higher. 5. pgfplots 1.5.1 interpretes circle- and ellipse radii as pgfplots coordinates (older versions used pgf unit vectors which have no direct relation to pgfplots). In other words: starting with version 1.5.1, it is possible to write \draw circle[radius=5] inside of an axis. This requires \pgfplotsset{compat=1.5.1} or higher. Without this compatibility setting, circles and ellipses use lowlevel canvas units of pgf as in earlier versions. 6. pgfplots 1.5 uses log origin=0 as default (which inuences logarithmic bar plots or stacked logarithmic plots). Older versions keep log origin=infty. This requires \pgfplotsset{compat=1.5} or higher. 7. pgfplots 1.4 has xed several smaller bugs which might produce dierences of about 12pt compared to earlier releases. This requires \pgfplotsset{compat=1.4} or higher. 8. pgfplots 1.3 comes with user interface improvements. The technical distinction between behavior options and style options of older versions is no longer necessary (although still fully supported). This is always activated. 9. pgfplots 1.3 has a new feature which allows to move axis labels tight to tick labels automatically. This is strongly recommended. It requires \pgfplotsset{compat=1.3} or higher. Since this aects the spacing, it is not enabled be default. 10. pgfplots 1.3 supports reversed axes. It is no longer necessary to use workarounds with negative units. Take a look at the x dir=reverse key. Existing workarounds will still function properly. Use \pgfplotsset{compat=1.3} or higher together with x dir=reverse to switch to the new version.

2.2.2

Old Features Which May Need Attention

1. The scatter/classes feature produces proper legends as of version 1.3. This may change the appearance of existing legends of plots with scatter/classes. 2. Starting with pgfplots 1.1, \tikzstyle should no longer be used to set pgfplots options. Although \tikzstyle is still supported for some older pgfplots options, you should replace any occurance of \tikzstyle with \pgfplotsset{ style name /.style={ key-value-list }} or the associated /.append style variant. See Section 4.18 for more detail. I apologize for any inconvenience caused by these changes. /pgfplots/compat=1.9|1.8|1.7|1.6|1.5.1|1.5|1.4|1.3|pre 1.3|default The preamble conguration\usepackage{pgfplots} \pgfplotsset{compat=1.9}

(initially default)

allows to choose between backwards compatibility and most recent features. Occasionally, you might want to use dierent versions in the same document. Then, provide\begin{figure} \pgfplotsset{compat=1.4} ... \caption{...} \end{figure}

10

CHAPTER 2. ABOUT PGFPLOTS: PRELIMINARIES in order to restrict the compatibility setting to the actual context (in this case, the figure environment). The the output of your .log le to see the suggested value for compat. Use \pgfplotsset{compat=default} to restore the factory settings. Although typically unnecessary, it is also possible to activate only selected changes and keep compatibility to older versions in general: /pgfplots/compat/path replacement= version /pgfplots/compat/labels= version /pgfplots/compat/scaling= version /pgfplots/compat/scale mode= version /pgfplots/compat/empty line= version /pgfplots/compat/plot3graphics= version /pgfplots/compat/bar nodes= version /pgfplots/compat/BB= version /pgfplots/compat/bar width by units= version /pgfplots/compat/general= version Let us assume that we have a document with \pgfplotsset{compat=1.3} and you want to keep it this way. In addition, you realized that version 1.5.1 supports circles and ellipses. Then, use 5 2 0 2 5 6 4 2 0 2 4 6% Preamble: \pgfplotsset{width=7cm,compat=1.9}

All of these keys accept the possible values of the compat key. The compat/path replacement key controls how radii of circles and ellipses are interpreted. The compat/labels key controls how axis labels are aligned: either uses adjacent to ticks or with an absolute oset. As of 1.8, it also enables an entirely new revision of the axis label styles. In most cases, you will see no dierence but it repairs axis lines=center in threedimensional axes. The compat/scaling key controls some bugxes introduced in version 1.4 and 1.6: they might introduce slight scaling dierences in order to improve the accuracy. The compat/plot3graphics controls new features for \addplot3 graphics. The compat/scale mode allows to enable/disable the warning The content of your 3d axis has CHANGED compared to previous versions because the axis equal and unit vector ratio features where broken for all versions before 1.6 and have been xed in 1.6. The compat/empty line allows to write empty lines into input les in order to generate a jump. This requires compat=1.4 or newer. See empty line for details. The compat/BB changes to bounding box to be tight even in case of hide axis. The compat/bar width by units allows to express bar width=1 (i.e. in terms of axis units). The compat/bar nodes activates presets for ybar stacked and nodes near coords. In addition, it enables stacked ignores zero for stacked bar plots. The compat/general key currently only activates log origin. The detailed eects can be seen on the beginning of this section. The value version can be default, a version number, and newest. The value default is the same

2.3. THE TEAM

11

as pre 1.3 (up to insignicant changes). The use of newest is strongly discouraged : it might cause changes in your document, depending on the current version of pgfplots. Please inspect your .log le to see suggestions for the best possible version.

2.3

The Team

pgfplots has been written mainly by Christian Feuers anger with many improvements of Pascal Wolkotte and Nick Papior Andersen as a spare time project. We hope it is useful and provides valuable plots. If you are interested in writing something but dont know how, consider reading the auxiliary manual TeX-programming-notes.pdf which comes with pgfplots. It is far from complete, but maybe it is a good starting point (at least for more literature).

2.4

Acknowledgements

I thank God for all hours of enjoyed programming. I thank Pascal Wolkotte and Nick Papior Andersen for their programming eorts and contributions as part of the development team. I thank J urnjakob Dugge for his contribution of hist/density, matlab scripts for \addplot3 graphics, excellent user forum help and helpful bug reports. I thank Stefan Tibus, who contributed the plot shell feature. I thank Tom Cashman for the contribution of the reverse legend feature. Special thanks go to Stefan Pinnow whose tests of pgfplots lead to numerous quality improvements. Furthermore, I thank Dr. Schweitzer for many fruitful discussions and Dr. Meine for his ideas and suggestions. Special thanks go to Markus B ohning for proofreading all the manuals of pgf, pgfplots, and PgfplotsTable. Thanks as well to the many international contributors who provided feature requests or identied bugs or simply improvements of the manual! Last but not least, I thank Till Tantau and Mark Wibrow for their excellent graphics (and more) package pgf and Tik Z, which is the base of pgfplots.

2.52.5.1

Installation and Prerequisites

Licensing

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A copy of the GNU General Public License can be found in the package le doc/latex/pgfplots/gpl-3.0.txt You may also visit http://www.gnu.org/licenses.

2.5.2

Prerequisites

pgfplots requires pgf. You should generally use the most recent stable version of PGF. pgfplots is used with \usepackage{pgfplots} \pgfplotsset{compat=yourversion} in your preamble (see Section 4.1 for information about how to use it with ConTEXt and plain TEX). The compat= yourversion entry should be added to activate new features, see the documentation of the compat key for more details. There are several ways how to teach TEX where to nd the les. Choose the option which ts your needs best.

12

CHAPTER 2. ABOUT PGFPLOTS: PRELIMINARIES

2.5.3

Installation in Windows

Windows users often use MikTEX which downloads the latest stable package versions automatically. You do not need to install anything manually here. However, MikTEX provides a feature to install packages locally in its own TEX-Directory-Structure (TDS). This is the preferred way if you like to install newer version than those of MikTEX. The basic idea is to unzip pgfplots in a directory of your choice and congure the MikTEX Package Manager to use this specic directory with higher priority than its default paths. If you want to do this, start the MikTEX Settings using Start Programs MikTEX Settings. There, use the Roots menu section. It contains the MikTEX Package directory as initial conguration. Use Add to select the directory in which the unzipped pgfplots tree resides. Then, move the newly added path to the lists top using the Up button. Then press Ok. For MikTEX 2.8, you may need to uncheck the Show MikTEX-maintained root directories button to see the newly installed path. MikTEX complains if the provided directory is not TDS conform (see Section 2.5.6 for details), so you cant provide a wrong directory here. This method does also work for other packages, but some packages may need some directory restructuring before MikTEX accepts them.

2.5.4

Installation of Linux Packages

At the time of this writing, I am unaware of pgfplots packages for recent stable Linux distributions. For Ubuntu, there are unocial Ubuntu Package Repositories which can be added to the Ubuntu Package Tools. The idea is: add a simple URL to the Ubuntu Package Tool, run update and the installation takes place automatically. These URLs are maintained as PPA on Ubuntu Servers. The pgfplots download area on sourceforge contains recent links about Ubuntu Package Repositories, go to http://sourceforge.net/projects/pgfplots/files and download the readme les with recent links.

2.5.5

Installation in Any Directory - the TEXINPUTS Variable

You can simply install pgfplots anywhere on your harddrive, for example into /foo/bar/pgfplots. Then, you set the TEXINPUTS variable to TEXINPUTS=/foo/bar/pgfplots//: The trailing : tells TEX to check the default search paths after /foo/bar/pgfplots. The double slash // tells TEX to search all subdirectories. If the TEXINPUTS variable already contains something, you can append the line above to the existing TEXINPUTS content. Furthermore, you should set TEXDOCS as well, TEXDOCS=/foo/bar/pgfplots//: so that the TEX-documentation system nds the les pgfplots.pdf and pgfplotstable.pdf (on some systems, it is then enough to use texdoc pgfplots). Please refer to your operating systems manual for how to set environment variables.

2.5.6

Installation Into a Local TDS Compliant texmf-Directory

pgfplots comes in a TEX Directory Structure (TDS) conforming directory structure, so you can simply unpack the les into a directory which is searched by TEX automatically. Such directories are ~/texmf on Linux systems, for example. Copy pgfplots to a local texmf directory like ~/texmf. You need at least the pgfplots directories tex/generic/pgfplots and tex/latex/pgfplots. Then, run texhash (or some equivalent path-updating command specic to your TEX distribution). The TDS consists of several sub directories which are searched separately, depending on what has been A requested: the sub directories doc/latex/ package are used for (L TEX) documentation, the sub-directories A doc/generic/ package for documentation which apply to L TEX and other TEX dialects (like plain TEX and ConTEXt which have their own, respective sub-directories) as well.

2.6. TROUBLESHOOTING ERROR MESSAGES

13

A Similarly, the tex/latex/ package sub-directories are searched whenever L TEX packages are requested. A The tex/generic/ package sub-directories are searched for packages which work for L TEX and other TEX dialects. Do not forget to run texhash.

2.5.7

Installation If Everything Else Fails...

If TEX still doesnt nd your les, you can copy all .sty and all .code.tex-les (perhaps all .def les as well) into your current projects working directory. In fact, you need everything which is in the tex/latex/pgfplots and tex/generic/pgfplots sub directories. Please refer to http://www.ctan.org/installationadvice/ for more information about package installation.

2.6

Troubleshooting Error Messages

This section discusses some problems which may occur when using pgfplots. Some of the error messages are shown in the index, take a look at the end of this manual (under Errors).

2.6.1

Problems with available Dimen-registers

To avoid problems with the many required TEX-registers for pgf and pgfplots, you may want to include \usepackage{etex} as rst package. This avoids problems with no room for a new dimen in most cases. It should work with any modern installation of TEX (it activates the e-TEX extensions).

2.6.2

Dimension Too Large Errors

The core mathematical engine of pgf relies on TEX registers to perform fast arithmetics. To compute 50 + 299, it actually computes 50pt+299pt and strips the pt sux of the result. Since TEX registers can only contain numbers up to 16384, overow error messages like Dimension too large occur if the result leaves the allowed range. Normally, this should never happen pgfplots uses a oating point unit with data range 10324 and performs all mappings automatically. However, there are some cases where this fails. Some of these cases are: 1. The axis range (for example, for x) becomes relatively small. Its no matter if you have absolutely small ranges like [1017 , 1016 ]. But if you have an axis range like [1.99999999, 2], where a lot of signicant digits are necessary, this may be problematic. I guess I cant help here: you may need to prepare the data somehow before pgfplots processes it. 2. This may happen as well if you only view a very small portion of the data range. This happens, for example, if your input data ranges from x [0, 106 ], and you say xmax=10. Consider using the restrict x to domain*= min : max key in such a case, where the min and max should be (say) four times of your axis limits (see page 328 for details).

3. The axis equal key will be confused if x and y have a very dierent scale. 4. You may have found a bug please contact the developers.

2.6.3

Restrictions for DVI-Viewers and dvipdfm

pgf is compatible with

latex/dvips, latex/dvipdfm, pdflatex,

. . .

14

CHAPTER 2. ABOUT PGFPLOTS: PRELIMINARIES

However, there are some restrictions: I dont know any DVI viewer which is capable of viewing the output of pgf (and therefor pgfplots as well). After all, DVI has never been designed to draw something dierent than text and horizontal/vertical lines. You will need to view the postscript le or the pdf-le. Then, the DVI/pdf combination doesnt support all types of shadings (for example, the shader=interp is only available for dvips, pdftex, dvipdfmx, and xetex drivers). Furthermore, pgf needs to know a driver so that the DVI le can be converted to the desired output. Depending on your system, you need the following options: latex/dvips does not need anything special because dvips is the default driver if you invoke latex. pdflatex will also work directly because pdflatex will be detected automatically. latex/dvipdfm requires to use

\def\pgfsysdriver{pgfsys-dvipdfm.def} %\def\pgfsysdriver{pgfsys-pdftex.def} %\def\pgfsysdriver{pgfsys-dvips.def} %\def\pgfsysdriver{pgfsys-dvipdfmx.def} %\def\pgfsysdriver{pgfsys-xetex.def} \usepackage{pgfplots}. The uncommented commands could be used to set other drivers explicitly. Please read the corresponding sections in [5, Section 7.2.1 and 7.2.2] if you have further questions. These sections also contain limitations of particular drivers. The choice which wont produce any problems at all is pdflatex.

2.6.4

Problems with TEXs Memory Capacities

pgfplots can handle small up to medium sized plots. However, TEX has never been designed for data plots you will eventually face the problem of small memory capacities. See Section 6.1 for how to enlarge them.

2.6.5

Problems with Language Settings and Active Characters

Both pgf and pgfplots use a lot of active characters which may lead to incompatibilities with other packages which dene active characters. Compatibility is better than in earlier versions, but may still be an issue. The manual compiles with the babel package for english and french, the german package does also work. If you experience any trouble, let me know. Sometimes it may work to disable active characters temporarily (babel provides such a command).

2.6.6

Other Problems

Please read the mailing list at http://sourceforge.net/projects/pgfplots/support. Perhaps someone has also encountered your problem before, and maybe he came up with a solution. Please write a note on the mailing list if you have a dierent problem. In case it is necessary to contact the authors directly, consider the addresses shown on the title page of this document.

Chapter 3

StepbyStep Tutorials3.1 Introduction

Visualization of data is often necessary and convenient in order to analyze and communicate results of research, theses, or perhaps just results. pgfplots is a visualization tool. The motivation for pgfplots is that you as enduser provide the data and the descriptions as input, and pgfplots takes care of rest such as choosing suitable scaling factors, scaling to a prescribed target dimension, choosing a good displayed range, assigning tick positions, drawing an axis with descriptions placed at appropriate places. pgfplots is a solution for an old problem of visualization in LaTeX: its descriptions use the same fonts as the embedding text, with exactly the same font sizes. Its direct embedding in LaTeX makes the use of LaTeXs powerful math mode as easy as possible: for any kind of axis descriptions up to userdened annotations. It features documentwide linestyles, color schemes, markers... all that makes up consistency. pgfplots oers highquality. At the same time, it is an embedded solution: it is largely independent of 3rd partytools, although it features import functions to benet from available tools. Its main goal is: you provide your data and your descriptions and pgfplots runs without more input. If you want, you can customize what you want.

3.2

Solving a Real UseCase: Function Visualization

In this section, we assume that you want to visualize two functions. The rst function is given by means of a data table. The second function is given by means of a math expression. We would like to place the two results sidebyside, and we would like to have proper alignment (whatever that means). As motivated, we have one data table. Let us assume that it is as shown below.x_0 f(x) # some comment line 3.16693000e-05 -4.00001451e+00 1.00816962e-03 -3.08781504e+00 1.98466995e-03 -2.88058811e+00 2.96117027e-03 -2.75205040e+00 3.93767059e-03 -2.65736805e+00 4.91417091e-03 -2.58181091e+00 5.89067124e-03 -2.51862689e+00 .... 9.89226496e-01 2.29825980e+00 9.90202997e-01 2.33403276e+00 9.91179497e-01 2.37306821e+00 9.92155997e-01 2.41609413e+00 9.93132498e-01 2.46412019e+00 9.94108998e-01 2.51860712e+00 9.95085498e-01 2.58178769e+00 9.96061999e-01 2.65733975e+00 9.97038499e-01 2.75201383e+00 9.98014999e-01 2.88053559e+00 9.98991500e-01 3.08771757e+00 9.99968000e-01 3.99755546e+00

Note that parts of the data le have been omitted here because it is a bit lengthy. The data le 15

16

CHAPTER 3. STEPBYSTEP TUTORIALS

(and all others referenced in this manual) are shipped with pgfplots; you can nd them in the subfolder doc/latex/pgfplots/plotdata.

3.2.1

Getting the Data Into TEX

Our rst step is to get the data table into pgfplots. In addition, we want axis descriptions for the x and y axes and a title on top of the plot. Our rst version looks like Inv. cum. normal 4 2 0 2 4 0 0.2 0.4 x The code listing already shows a couple of important aspects:A 1. As usual in L TEX, you include the package using \usepackage{pgfplots}.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

2. Not so common is \pgfplotsset{compat=1.5} . A statement like this should always be used in order to (a) benet from a more-or-less recent feature set and (b) avoid changes to your picture if you recompile it with a later version of pgfplots. Note that pgfplots will generate some suggested value into your log le (since 1.6.1). The minimum suggested version is \pgfplotsset{compat=1.3} as this has great eect on the positioning of axis labels. 3. pgfplots relies on Tik Zand pgf. You can say it is a third party package on top of Tik Z/pgf. Consequently, we have to write each pgfplots graph into a Tik Z picture, hence the picture environment given by \begin{tikzpicture} ... \end{tikzpicture}. 4. Each axis in pgfplots is written into a separate environment. In our case, we chose \begin{axis} ... \end{axis} as this is the environment for a normal axis. There are more axis environments (like the \begin{loglogaxis} ... ment for logarithmic axes). \end{loglogaxis} environ-

Although pgfplots runs with default options, it accepts keys. Lots of keys. Typically, you provide all keys which you want to have in square brackets somewhere and ignore all other keys. Of course, the main diculty is to get an overview over the available keys and to nd out how to use them. This reference manual and especially its Section 4 has been designed for online browsing: it contains hundreds of cross-referenced examples. Opening the manual in a pdf viewer and searching it for keywords will hopefully jump to a good match from which you can jump to the reference section (for example about tick labels, tick positions, plot handlers etc). It is (and will always be) the most reliable source of detail information about all keys. Speaking about the reference manual: note that most pdf viewers also have a function to jump back to the page before you clicked on a hyperlink (for Acrobat Reader, open the menu View / Toolbars / More Tools and activate the Previous View and Next View buttons which are under Page Navigation Toolbar). Note that the code listing contains two sets of keys: the rst is after \begin{axis}[ .... ] and the second right after \addplot[...]. Note furthermore that the option list after the axis has been

3.2. SOLVING A REAL USECASE: FUNCTION VISUALIZATION

17

indented: each option is on a separate line, and each line has a tab stop as rst character. This is a good practice. Another good practice is to place a comma after the last option (in our case, after the value for ylabel). This allows to add more keys easily and you wont forget the comma. It does not hurt at all. The second set of keys after \addplot shows that indentation and trailing comma a really just a best-practice: we simply said \addplot[blue], meaning that the plot will be placed in blue color, without any plot mark. Of course, once another option would be added here, it would be best to switch to indentation and trailing comma:\addplot[ blue, mark=*, ] table {invcum.dat};

5. Inside of an axis, pgfplots accepts an \addplot ...

; statement (note the nal semicolon).

In our case, we use \addplot table: it loads a table from a le and plots the rst two columns. There are, however, more input methods. The most important available inputs methods are \addplot expression (which samples from some mathematical expression) and \addplot table (loads data from tables), and a combination of both which is also supported by \addplot table (loads data from tables and applies mathematical expressions). Besides those tools which rely only on builtin methods, there is also an option to calculated data using external tools: \addplot gnuplot which uses gnuplot as desktop calculator and imports numerical data, \addplot shell (which can load table data from any system call), and the special \addplot graphics tool which loads an image together with meta data and draws only the associated axis. In our axis, we nd a couple of tokens: the rst is the mandatory \addplot token. It starts a further plot. The second is the option list for that plot, which is delimited by square brackets (see also the notes about best-practices above). The name option list indicates that this list can be empty. It can also be omitted completely in which case pgfplots will choose an option list from its current cycle list (more about that in a dierent lecture). The next token is the keyword table. It tells pgfplots that table data follows. The keyword table also accepts an option list (for example, to choose columns, to dene a dierent col sep or row sep or to provide some math expression which is applied to each row). More on that in a dierent lecture. The next token is {invcum.dat}: an argument in curly braces which provides the table data. This argument is interpreted by plot table. Other input types would expect dierent types of arguments. In our case, the curly braces contain a le name. Plot table expects either a le name as in our case or a so-called inline table. An inline table means that you would simply insert the contents of your le inside of the curly braces. In our case, the table is too long to be inserted into the argument, so we place it into a separate le. Finally, the last (mandatory!) token is a semicolon. It terminates the \addplot statement. 6. Axis descriptions can be added using the keys title, xlabel, ylabel as we have in our example listing. pgfplots accepts lots of keys and sometimes it is the art of nding just the one that you were looking for. Hopefully, a search through the table of contents of the reference manual and/or a keyword search through the entire reference manual will show a hit.

3.2.2

FineTuning of the First Picture

While looking at the result of Section 3.2.1, we decide that we want to change something. First, we decide that the open ends on the left and on the right are disturbing (perhaps we have a strange taste or perhaps we know in advance that the underlying function is not limited to any interval). Anyway, we would like to show it only in the y interval from 3 to +3. We can do so as follows:

2 0 0.2 0.4 x We added three more options to the option list of the axis. The rst pair is ymin=-3 and ymax=3. Note that we have placed them on the same line although we said the each should be on a separate line. Line breaks are really optional; and in this case, the two options appear to belong together. They dene the display limits. Display limits dene the window of the axis. Note that any \addplot statements might have more data (as in our case). They would still generate graphics for their complete set of data points! The keys ymin,ymax,xmin,xmax control only the visible part, i.e. the axis range. Everything else is clipped away (by default). The third new option is minor y tick num=1 which allows to customize minor ticks. Note that minor ticks are only displayed if the major ticks have the same distance as in our example. Note that we could also have modied the width and/or height of the gure (the keys have these names). We could also have used one of the predened styles like tiny or small in order to modify not just the graphics, but also use dierent fonts for the descriptions. We could also have chosen to adjust the unspecied limits: either by xing them explicitly (as we did for y above) or by modifying the enlargelimits key (for example using enlargelimits=false). We are now satised with the rst picture and we would like to add the second one. 0.6 0.8 1

3.2.3

Adding the Second Picture with a Dierent Plot

As motivated, our goal is to have two separate axes placed sidebyside. The second axis should show a function given as math expression. More precisely, we want to show the density function of a normal distribution here (which is just a special math expression). We simply start a new tikzpicture and insert a new axis environment (perhaps by copy-pasting our existing one). The \addplot command is dierent, though: 400 300 200 100 2 0 2 103% Preamble: \pgfplotsset{width=7cm,compat=1.9}

We see that it has an axis environment with an empty option list. This is quite acceptable: after all, it is to be expected that we will add options eventually. Even if we dont: it does not hurt. Then, we nd the expected \addplot statement. As already explained, \addplot statements initiate a new plot. It is followed by an (optional) option list, then by some keyword which identies the way input coordinates are provided, then arguments, and nally a semicolon. In our case, we nd an option list which results in a red plot. The two keys domain and samples control how our math expression is to be evaluated: domain denes the sampling interval in the form a:b and samples=N expects the number of samples inserted into the sampling

3.2. SOLVING A REAL USECASE: FUNCTION VISUALIZATION

19

interval. Note that domain merely controls which samples are taken; it is independent of the displayed axis range (and both can dier signicantly). If the keyword dening how coordinates are provided is missing, pgfplots assumes that the next argument is a math expression. Consequently, the rst token after the option list is a math expression in curly braces. We entered the density function of a normal distribution here (compare Wikipedia). Note that the axis has an axis multiplier: the x tick labels have been chosen to be 2, 0, and 2 and an extra x tick scale label of the form 103 . These tick scale labels are quite convenient are are automatically deduced from the input data. We will see an example with the eects of scaled x ticks=false at the end of this tutorial. Inside of the math expression, you can use a lot of math functions like exp, sin, cos, sqrt, you can use exponents using the a^b syntax, and the sampling variable is x by default. Note, however, that trigonometric functions operate on degrees ! If you need to sample the sinus function, you can use \addplot[domain=0:360] {sin(x)};. This is quite uncommon. You can also use \addplot[domain=0:2*pi] {sin(deg(x)};. This samples radians (which is more common). But since the math parser expects degrees, we have to convert x to degrees rst using the deg() function. The math parser is written in TEX(it does not need any third-party tool). It supports the full range of a double precision number, even though the accuracy is about that of a single precision number. This is typically more than sucient to sample any function accurately. If you ever encounter diculties with precision, you can still resort to \addplot gnuplot in order to invoke the external tool gnuplot as coordinate calculator. The experienced reader might wonder about constant math expressions domain=-3e-3:3e-3, 2e-3^2, and 1e-3 rather than some variable name like mu or sigma. This is actually a matter of taste: both is supported and we will switch to variable names in the next listing. The main part of our step here is still to be done: we wanted to place two gures sidebyside. This can be done as follows: Inv. cum. normal 400 2

The listing above shows the two separate picture environments: the rst is simply taken as-is from the previous step and the second is new. Note that both are simply placed adjacent to each other: we only inserted comment signs to separate them. This approach to place graphics sidebyside is common in TEX: it works for \includegraphics in the same way. You could, for example, write\includegraphics{image1}% % \hskip 10pt % insert a non-breaking space of specified width. % \includegraphics{image2}

to place two graphics next to each other. This here is just the same (except that our graphics occupy more code in the .tex le). Note that there is also a comment sign after \end{tikzpicture}. This is not just a best-practice: it is necessary to suppress spurious spaces! In TEX, every newline character is automatically converted to a white space (unless you have an empty line, of course). In our case, we want no white spaces. In our second picture, we see the eects of switch our math expression to constant denitions as promised earlier. The interesting part starts with two constants which are dened by means of two \newcommand s: we dene \MU to be 0 and \SIGMA to be 1e-3. This is one way to dene constants (note that such a denition of constants should probably introduce round braces if numbers are negative, i.e. something like \newcommand\negative{(-4)}).

3.2.4

Fixing the Vertical Alignment and Adjusting Tick Label Positions

Note that even though our individual pictures look quite good, the combination of both is not properly aligned. The experienced reader identies the weak point immediately: the bounding box of the two images diers, and they are aligned at their baseline (which is the bottom edge of the picture). In particular, the xlabel=$x$ of the left picture and the automatically inserted scaling label \cdot 10^{-3} of the right picture cause an unwanted vertical shift. We want to x that in the next step. Besides the bad alignment, we nd it a little bit misleading that the axis descriptions of the second picture are between both pictures. We would like to move them to the right. Let us present the result rst:

This listing has a couple of modications. The most important one is the we added an option list to the tikzpicture environment: the baseline option. This option shifts the picture up or down such that the canvas coordinate y = 0 is aligned at the baseline of the surrounding text. In pgfplots, the y = 0 line is the lower edge of the box. This simple feature allows both axes to be aligned vertically: now, their boxes are aligned rather than the lower edges of their bounding boxes. The option baseline needs to be provided to all pictures for which this shifting should be done in our case, to all which are to be placed in one row. Keep in mind that it is an option for \begin{tikzpicture}. The second change is rather simple: we only added the option yticklabel pos=right to the second axis. This moves all tick labels to the right, without changing anything else. Note that there is much more to say about alignment and bounding box control. After all, we did not really change the bounding box - we simply moved the pictures up or down. There is also the use-case where we want horizontal alignment: for example if the two pictures should be centered horizontally or if they should be aligned with the left- and right end of the margins. The associated keys \begin{tikzpicture}[trim axis left, trim axis right] and \centering are beyond the scope of this tutorial, please refer to Section 4.19 for details.

3.2.5

Satisfying Dierent Tastes

We are now in a position where the gures as such are in a good shape. However, an increase in knowledge will naturally lead to an increase in questions. Some of these questions will be part of other how-to lectures. But the most commonly asked questions are addressed here (feel free to email some more if you believe that I should include another hotspot):

22 1. How can I get rid of that 103 -label? 2. How can I modify the number printing?

CHAPTER 3. STEPBYSTEP TUTORIALS

3. How can I have one single line per axis rather than a box? This here gives brief hints where to look in this reference manual for more details. We modify the appearance of the second picture according to the questions above:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The appearance of the axes as such can be controlled by means of the axis lines key. It accepts the values left, right, box, center, none (and also top, bottom, middle which are aliases). The xticklabel style key modies a predened style (note the use of indentation here!). A style is a collection of keys which are applied in a specic context. Styles are very useful and are widely used by pgfplots. In our case, we adjust a couple of options like rotation, alignment (the anchor option), and number printing options. The precise details of these individual options is beyond the scope of this tutorial. The keys actually belong to Tik Z - and the Tik Z manual is the reference for these keys (although pgfplots also covers most of the topics). The complete set of number printing options is available in both the Tik Z manual [5] and the manual for PgfplotsTable which is shipped with pgfplots. A brief extract can be found in Section 4.13.

3.2.6

Finishing Touches: Automatic Generation of Individual Pdf Graphics

As last step in this lecture, I would like to talk about one technical topic. Typically, a TEXdocument starts quite simple: a little bit of text, perhaps one or two pictures. But they tend to grow. And eventually, you will encounter one of the weak points of pgfplots: the graphics are involved and TEXconsumes a lot of time to generate them. Especially if it keeps regenerating them even though they did not change at all. The fact that we need to rerun the pdatex processor all the time makes things worse. Fortunately, there are solutions. A simple solution is: why cant we write each individual graphics into a separate .pdf le and use \includegraphics to include it!? The answer is: yes, we can. And it is surprisingly simple to do so. In order to convert every tikzpicture environment automatically to an external graphics without changing any line of code in the TEXle, we can simply write the following two lines into the documents preamble:\usepgfplotslibrary{external} \tikzexternalize ... \begin{document} ... \end{document}

But now, we have to provide a command-line switch to pdatex :

pdflatex -shell-escape myfile.tex

This works out-of-the box with pdflatex. If you use latex/dvips, lualatex, dvipdfm or any other TEXderivate, you need to modify the option \tikzexternalize[system call=....] (which is, unfortunately, system-dependent, especially for the postscript variants).

0.002

0.000

3.3. SOLVING A REAL USECASE: SCIENTIFIC DATA ANALYSIS

23

It might be too much to discuss how to dene individual le names or how to modify the le name generation strategy. There is also the \tikzexternalize[mode=list and make] feature which generates a GNU Make le to allow \label/\ref to things inside of the external graphics and which supports the generation of all images in parallel (if you have a multi-core PC). Details of the external library can be found in Section 7.1 (but only a brief survey) and, in all depth, in the Tik Z reference manual [5].

3.2.7

Summary

We learned how to create a standard axis, and how to assign basic axis descriptions. We also saw how to plot functions from a data table (in our case a tab-separated le, but other delimiters as in csv les are also supported) and from math expressions. We saw that pgfplots does a reasonable good job at creating a fully-featured axis automatically (like scaling the units properly, choosing tick positions and labels). We also learned how to improve vertical alignment and how to customize the appearance of an axis. Next steps might be how to draw multiple plots into the same axis, how to employ scatter plots of pgfplots, how to generate logarithmic axes, or how to draw functions of two variables. Some of these aspects will be part of further how-to lectures.

Finally, the last table is data_d4.dat

What we want is to produce three plots, each dof versus l2_err, in a loglog plot. We expect that the result is a line in a loglog plot, and we are interested in its slope log e(N ) = a log(N ) because that characterizes our experiment.

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CHAPTER 3. STEPBYSTEP TUTORIALS

3.3.1

Getting the Data into TeX

Our rst step is to get one of our data tables into pgfplots. In addition, we want axis descriptions for the x and y axes and a title on top of the plot. Our rst version looks like Convergence Plot 101 102 L2 Error 103 104 105 101 102 103 Degrees of freedom 104% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Our example is similar to that of the lecture in Section 3.2.1 in that it denes some basic axis descriptions by means of title, xlabel, and ylabel and provides data using \addplot table. The only dierence is that we used \begin{loglogaxis} instead of \begin{axis} in order to congure logarithmic scales on both axes. Note furthermore that we omitted any options after \addplot. As explained in Section 3.2.1, this tells pgfplots to consult its cycle list to determine a suitable option list.

3.3.2

Adding the Remaining Data Files of Our Example.

; command so we can just add our remaining data les:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

You might wonder how pgfplots chose the dierent line styles. And you might wonder how to modify them. Well, if you simply write \addplot without options in square brackets, pgfplots will automatically choose styles for that specic plot. Here automatically means that it will consult its current cycle list: a list of predened styles such that every \addplot statement receives one of these styles. This list is customizable to a high degree. Instead of the cycle list, you can easily provide style options manually. If you write \addplot[ options ] ..., pgfplots will only use options and will ignore its cycle list. If you write a plus sign before the square brackets as in \addplot+[ options ] ..., pgfplots will append options to the automatically assigned cycle list.

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3.3.3

Add a Legend and a Grid

A legend is a text label explaining what the plots are. A legend can be provided for one or more \addplot statements using the legend entries key: Convergence Plot 101 102 L2 Error 103 104 105 101 102 103 104 105 Degrees of freedom d=2 d=3 d=4% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we assigned a comma-separated list of text labels, one for each of our \addplot instructions. Note the use of math mode in the text labels. Note that if any of your labels contains a comma, you have to surround the entry by curly braces. For example, we could have used legend entries={{$d=2$},{$d=3$},{$d=4$}} pgfplots uses these braces to delimit arguments and strips them afterwards (this holds for any option, by the way). Our example also contains grid lines for which we used the grid=major key. It activates major grid lines in all axes. You might wonder how the text labels map to \addplot instructions. Well, they are mapped by index. The rst label is assigned to the rst plot, the second label to the second plot and so on. You can exclude plots from this counting if you add the forget plot option to the plot (using \addplot+[forget plot], for example). Such plots are excluded from both cycle lists and legends.

3.3.4

Add a Selected Fit-line

Occasionally, one needs to compute linear regression lines through input samples. Let us assume that we want to compute a t line for the data in our fourth data table (data_d4.dat). However, we assume that the interesting part of the plot happens if the number of degrees of freedom reaches some asymptotic limit (i.e. is very large). Consequently, we want to assign a high uncertainty to the rst points when computing the t line. pgfplots oers to combine table input and mathematical expressions (note that you can also type pure mathematic expressions, although this is beyond the scope of this example). In our case, we employ this feature to create a completely new column - the linear regression line:

Note that we added a further package: pgfplotstable. It allows to postprocess tables (among other things. It also has a powerful table typesetting toolbox which rounds and formats numbers based on your input CSV le). Here, we added a fourth plot to our axis. The rst plot is also an \addplot table statement as before and we see that it loads the data le data_d4.dat just like the plot before. However, it has special keys which control the coordinate input: x=dof means to load x coordinates from the column named dof. This is essentially the same as in all of our other plots (because the dof column is the rst column). It also uses y={create col/.......}. This lengthy statement denes a completely new column. The create col/linear regression prex is a key which can be used whenever new table columns can be generated. As soon as the table is queried for the rst time, the statement is evaluated and then used for all subsequent rows. The argument list for create col/linear regression contains the column name for the function values y=l2_err which are to be used for the regression line (the x arguments are deduced from x=dof as you guessed correctly). The variance list option is optional. We use it to assign variances (uncertainties) to the rst input points. More precisely: the rst encountered data point receives a variance of 1000, the second 800, the third 600, and so on. The number of variances does not need to match up with the number of points; pgfplots simply matches them with the rst encountered coordinates. Note that since our legend entries key contains only three values, the regression line has no legend entry. We could easily add one, if we wanted. We can also use \addplot+[forget plot] table[....] to explicitly suppress the generation of a legend as mentioned above. Whenever pgfplots encounteres mathematical expressions, it uses its built-in oating point unit. Consequently, it has a very high data range and a reasonable precision as well.

3.3.5

Add an Annotation using Tik Z: a Slope Triangle

Often, data requires interpretation and you may want to highlight particular items in your plots. This highlight particular items requires to draw into an axis, and it requires a high degree of exibility. Users of Tik Z would say that Tik Z is a natural choice and it is. In our use-case, we are interested in slopes. We may want to compare slopes of dierent experiments. And we may want to show selected absolute values of slopes. Here, we use Tik Z to add custom annotations into a pgfplots axis. We choose a particular type of a custom annotation: we want to mark two points on a line plot. One way to do so would be to determine the exact coordinates and to place a graphical element at this coordinate (which is possible using the pgfplots coordinate system axis cs and \draw .... (axis cs:1e4,1e-5) ... ). Another (probably simpler) way is to use the pos feature to identify a position 25% after the line started. Based on the result of Section 3.3.4, we nd

The example is already quite involved since we added complexity in every step. Before we dive into the details, let us take a look at a simpler example: 101 102 103 104 105 101 102 103 104 Special.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we see two annotation concepts oered by pgfplots : the rst is to insert drawing commands right after an \addplot command (but before the closing semicolon). The second is to add standard Tik Z commands, but use designated pgfplots coordinates. Both are Tik Z concepts. The rst is what we want here: we want to identify two coordinates which are somewhere on the line. In our case, we dene two named coordinates: coordinate A at 25% of the line and coordinate B at 40% of the line. Then, we use \draw (A) -| (B) to draw a triangle between these two points. The second is only useful if we know some absolute coordinates in advance. Coming back to our initial approach with the regression line, we see that it uses the rst concept: it introduces named coordinates after \addplot, but before the closing semicolon. The statement \xdef\slope introduces a new macro. It contains the (expanded due to the eXpanded DEFinition) value of \pgfplotstableregressiona which is the slope of the regression line. In addition to the slope triangle, we also add a node in which we typeset that value using \pgfmathprintnumber. Note that the example above is actual a happy case: it can happen easily that labels which are added inside of the axis environment are clipped away:

28101 102 103 104 105 101 102 103 104

CHAPTER 3. STEPBYSTEP TUTORIALS

The example above combines the pos label placement with the nodes label. Note that the small style tiny installs a pgfplots preset which is better suited for very small plots it is one of the many supported scaling parameters. The problem here is apparent: the text of our extra node is clipped away. Depending on your data, you have a couple of solutions here: use clip=false to disable clipping of plot paths at all, use clip mode=individual to enable clipping only for plot paths, draw the node outside of the axis environment but inside of the picture environment.

Note that this approach in which the nodes are placed before the closing semicolon implies that nodes inherit the axis line style and color.

3.3.6

Summary

We learned how to dene a (logarithmic) axis, and how to assign basic axis descriptions. We also saw once more how to use one or more\addplot table commands to load table data into pgfplots . We took a brief look into regression and Tik Z drawing annotations. We also encountered the tiny style which is one of the ways to customize the size of an axis. Others are width, height, the other predened size styles like normalsize, small, or footnotesize, and the two dierent scaling modes /pgfplots/scale and /tikz/scale (the rst scales only the axis, the second also the labels). Next steps might be how to visualize functions using line plots, how to align adjacent graphics properly (even if the axis descriptions vary), how to employ scatter plots of pgfplots , or how to draw functions of two variables.

3.4

UseCases involving Scatter Plots

Assuming that we are moreorless familiar with the basics of the preceding tutorials, we would like to draw a scatter plot. A scatter plot is one in which markers indicate the important information. There are many dierent kinds of scatter plots and this section covers a couple of them.

3.4.1

Scatter Plot Usecase A

In this subsection, we address the following scatter plot usecase: assume that we are given a couple of special (x, y ) coordinates along with color data at every vertex. We would like to draw markers at the positions and choose individual colors depending on the color data.

6 4 2 0 0 0.2 0.4 0.6 0.8 1

Here, the only nontrivial variation is the option only marks which is given after the plus sign. Keep in mind that \addplot+[ options ] means that pgfplots shall combine the set of options of its cycle list with options . In our case, only marks does what it says. The only marks plot handler is the most simple scatter plot: it uses the same color for every marker. Note that \addplot table takes the rst column as x and the second as y (which matches our input le perfectly). Fine Tuning We agree that our initial import has unsuitable displayed limits: there is too much white space around the interesting plot area. In addition, the markers overlap because they are too large. We can modify the appearance as follows: 6% Preamble: \pgfplotsset{width=7cm,compat=1.9}

As before, we assume that we add more options after \begin{axis}. Consequently, we introduced suitable indentation and a trailing comma after the option. Note that enlargelimits is typically active; it means that pgfplots increases the displayed range by 10% by default. Deactivating it produces tight limits according to the input data.

30

CHAPTER 3. STEPBYSTEP TUTORIALS Our second option is mark size using an absolute size (about the radius or half size of the marker).

Color Coding According To Input Data We are quite close to our goal, except for the colors. As discussed, our input le contains three columns and the third one should be used to provide color information. In our case, the data le has a column named f(x). 6 0

We added a couple of options to our example: the options scatter, and point meta, colorbar. The option scatter has a slightly misleading name as we already had a scatter plot before we added that option. It activates scatter plots with individual appearance: without further options, it chooses individual colors for every marker. The individual colors are based on something which is called point meta in pgfplots. The point meta is typically a scalar value for every input coordinate. In the default conguration , it is interpreted as color data for the coordinate in question. This also explains the other option: point meta=... tells pgfplots which values are to be used to determine colors. Note that the default value of point meta is to use the y coordinate. In our case, we have a complicated math expression which is related to our input le: it contains small quantities in column f(x) which are based shown on a logarithmic scale as their dier over a huge range. Since a logarithm must not have a non-positive argument, we have 106 + abs( ) as expression which ensures that the argument is never smaller than 10^{-6} and that is is positive. The divider /ln(10) means that we have logarithms base 10. But the key point of the whole complicated expression can be summarized as follows: 1. We can use \thisrow{ column name } to refer to table columns. Here, this row means to evaluate the table for the data point which is being read from the current row. 2. We can combine \thisrow with any complicated math expression. The third new option colorbar activates the color bar on the right hand side (as you guessed correctly). We see that the smallest value is 6 which corresponds to our value 1e-6 in the math expression. You might wonder how a scalar value (the number stored in the f(x) column) results in a color. pgfplots computes the minimum and maximum value of all such numbers. Then, it maps every number into a colormap. A colormap denes a couple of colors and interpolates linearly between such colors. That means that the smallest value of point meta is mapped to the rst color in a colormap whereas the largest value of point meta is mapped to the last color in the colormap. All others are mapped to something inbetween.

3.4. USECASES INVOLVING SCATTER PLOTS More information about colormap and point meta can be found in Section 4.7.6 and in Section 4.8.

31

3.4.2

Scatter Plot Usecase B

As already mentioned, there are various usecases for scatter plots. The default conguration of the scatter key is to read numeric values of point meta and choose colors by mapping that value into the current colormap. A dierent application would be to expect symbolic input (some string) and choose dierent markers depending on that input symbol. Suppose that you are given a sequence of input coordinates of the form (x, y ) class label and that you want to choose marker options depending on the class label . A pgfplots solution could be% Preamble: \pgfplotsset{width=7cm,compat=1.9}

As in our previous usecase in Section 3.4.1, we have the options scatter, only marks, and a conguration how to retrieve the point meta values by means of the meta key. One new key is point meta=explicit symbolic: it tells pgfplots that any encountered values of point meta are to be interpreted as string symbols. Furthermore, it tells pgfplots that the every input coordinate comes with an explicit value (as opposed to a common math expression, for example). The other dierent option is scatter/classes. As you guessed from the listing, it is a map from string symbol to marker option list. This allows to address such usecases in a simple way. This example has actually been replicated from the reference manual section for scatter/classes.

3.4.3

Scatter Plot Usecase C

Finally, this tutorial sketches a further usecase for scatter plots: given a sequence of coordinates (x, y ) with individual string labels, we want to draw the string label at the designated positions. This can be implemented by means of the nodes near coords feature of pgfplots, which is actually based on scatter:

In this case, we have point meta=explicit symbolic in order to express the fact that our labels are of textual form (see the reference manual section for nodes near coords for applications of numeric labels). The remaining stu is done by the implementation of nodes near coords. Note that enlarged the axis limits somewhat in order to include the text nodes in the visible area. There is much more to say about scatter plots, and about nodes near coords. Please consider this subsection as a brief pointer to Section 4.5.10 in the reference manual.

3.4.4

Summary

We learned how to generate scatter plots with single color using only marks, scatter plots with individually colored markers using the scatter key, scatter plots with specic marker styles depending on some class label using scatter/classes and text nodes using nodes near coords. Furthermore, we introduced the concept of point meta data: once as (scalar valued) color data, once as symbolic class label and once as text label. There is much more to say, especially about point meta which is introduced and explained in all depth in Section 4.8. There is also more to say about scatter plots, for example how to generate scatter plots with individually sized markers and/or colors (by relying on \pgfplotspointmetatransformed, see the reference manual section for visualization depends on). In addition, scatter plots can be customized to a high degree which is explained in Section 4.5.10.

3.5

Solving a Real UseCase: Functions of Two Variables

In this tutorial, we assume that we have two functions for which we seek a plot: the rst is a sampled function given by a huge data le and the second is the math expression g (x, y ) = exp(x2 y 2 ) x. Our rst function actually consists of two data les: the rst le contains some scattered data which is used to discretized (sample) a function and the second le contains data for the function as such. Our requirement here is two draw two graphs into the same axis: one in which the function is plotted as a smooth, colored surface and one in which the scattered data le should be on top of the surface because it provides more detail how the function was represented in the computer. The second function which is given as math expression should be visualized using a contour plot.

3.5.1

Surface Plot from Data File

Our rst step is to load the data le and to plot a surface. Clearly, functions of two variables require a more sophisticated input format: they are typically sampled on a unied grid with n m points, i.e. n points for x and m points for y , resulting in a total of matrix with n m values fij = f (xi , yi ). How can we read matrix data? And what if you have more than just the z value? A standard way is to write the matrix to a table, either in rowwise ordering or in columnwise ordering (both are common). Here, we assume that our function values are written to a table in which the y values vary from line to line. Here is an extract of the data le (which is too large to list it here): # ordering = colwise , number points =1089 ,

0.03125 0 3.0517578 e -05 5 1 0.03125 0.19634954 0.030093496 5 1 0.03125 0.39269908 0.1146012 5 1 0.03125 0.58904862 0.24129102 5 1 0.03125 0.78539816 0.38946059 5 1 0.03125 0.9817477 0.53949733 5 1 . . . Note that the data le (and all others referenced in this manual) are shipped with pgfplots; you can nd them in the subfolder doc/latex/pgfplots/plotdata. The input le contains x0 , x1 , and f (x0 , x1 ) in columns named x_0, x_1, and f(x), respectively. In addition, it contains some meta data which is irrelevant for us here. Note that our input le contains empty lines whenever x_0 changes. This is a common data format which simplies the detection of scanline length. A scanline is one line in the input matrix, for example the line consisting of all points with x0 = 0. With such scanlines, pgfplots can automatically deduce the size of the input matrix. In order to plot the le as a surface, we proceed as in the previous example by using \addplot table. However, we have to use \addplot3 to indicate that a threedimensional result is expected:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 6 4 0.2 0.4 0.6 0.8 2 1 0

The example looks familiar compared to our results of the preceding tutorials: a tikzpicture environment containing an axis environment and the mentioned \addplot3 command. The option list contains surf, which tells pgfplots how to visualize the input data. The key mesh/ordering=y varies tells pgfplots how to decode the input matrix. This is important; otherwise pgfplots would have chosen x varies which does not match our le. Note that we there is no need to congure either mesh/rows= N or mesh/cols= N here because these parameters are automatically deduced from the scan line lengths marked by empty lines in our input le. Since our \addplot3 table statement does not contain any hints which columns should be plotted, pgfplots simply plots the rst three columns against each other. The colors of a surf plot are chosen from the function values (unless you congure some other value for point meta; this is similar to the scatter plot example). In case of a function of two variables, the function value is the third column.

3.5.2

FineTuning

In order to stress how colors are to be mapped to values, we add a color bar. In addition, we rotate the view a little bit and add axis labels. Furthermore, we would like to have a smooth color mapping. We end up at

Here, view/h rotates the horizontal parts of the view (only). It chooses a new view angle for the orthographic projection. As you guessed, there is also a view/v key and a view={ h }{ v } variant. The key colorbar horizontal is a style which activates a colorbar and congures it to be displayed horizontally. The labels are placed using xlabel and ylabel as we saw it before for visualizations of one dimensional functions. A Colorbar uses the current colormap and adds axis descriptions to show how values are mapped to colors. The shader=interp key activates a smooth color interpolation.

3.5.3

Adding Scattered Data on Top of the Surface

As motivated earlier, we have a second data set, one which characterizes how the function has been represented in some computer simulation. We would like to add the second data set as scatter plot on top of the function. The data set as such is the very same as the one used in Section 3.4.1, so we do not need to list it here again. However, we have to include the twodimensional scatter data into the threedimensional axis in a suitable way. We chose to place it on a xed z value as follows:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Now, we have two \addplot3 table statements in the same axis. None of them uses the cycle list as we used explicit option lists. The rst is our surface plot. Note that it is plotted before the scatter plot: pgfplots cannot handle depth information between adjacent \addplot statements. It does, however, handle z buffer information for data of a single \addplot statement. The second plot is our scatter plot: we recognize only marks and mark size from Section 3.4.1. In addition, we congured some color and marker options. An important aspect is \addplot3 table[z expr=1.2] it tells pgfplots how to choose z values for the input le (otherwise, pgfplots would have used the third column of that le). This is a convenient way to insert twodimensional data into a threedimensional axis, provided you have table data. There is also a

3.5. SOLVING A REAL USECASE: FUNCTIONS OF TWO VARIABLES

35

dierent way which works for both tables and math expressions (or other input types). This dierent way is to install a z filter, but that is beyond the scope of this tutorial for now.

3.5.4

Computing a Contour Plot of a Math Expression

This section addresses the second part of our usecase example: a function of two variables given by a math expression. Our function of interest is x exp(x2 y 2 ). We start as in our tutorial for onedimensional functions given by a math expression (compare Section 3.2.3): by using an \addplot statement which is followed by a math expression in curly braces. However, we rely on \addplot3 as in the preceding section: x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0.4 0.2 0 0.2 0.4 4 2 0 0 2 5

Our example contains a basic axis environment with title, xlabel, ylabel and the small key which are already known from the preceding tutorials. The \addplot3 has no options and is immediately followed by the math expression. The absence of options tells pgfplots to rely on its cycle list. This, in turn congures mark=* with blue color and a line plot. A line plot combined with \addplot3 is of limited use; it merely connects all incoming points. Since points are sampled as a matrix (linebyline). Our next step will be to dene a suitable plot handler. Note, however, that our math expression depends on x and y. These two variables are the sampling variables of pgfplots in its default congures: both are sampled in the domain of interest using the correct number of samples. The \addplot3 statement takes care of computing N M points in the correct sequence where N is the number of samples for x and M is samples y, the number of samples used for y . We can see that our sampling domain is too large. Switching to a smaller domain focusses on the interesting parts of our function: x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we introduced an option list after \addplot3. Since we provided the option list without the leading plus sign +, pgfplots does not consider its cycle list at all (and switches o marks and the default color settings). We added domain and domain y in order to restrict the sampling domain in a suitable way. If we would have omitted domain y, the y domain would use the same value as the x domain. As you might have guessed, the surf key has the main usecase of providing a connection to the previous tutorial section: it is one of the natural visualizations for functions of two variables. As in the preceding

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CHAPTER 3. STEPBYSTEP TUTORIALS

section, the color has been deduced from the function value z = f (x, y ) (more precisely, by relying on the default conguration point meta=f(x)). The next step is to switch to contour plots by replacing surf by contour gnuplot: x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Now, we have a contour plot although it is not quite what we had in mind. First, there are so few contour lines that it is hard to see anything (especially since the line width is too small). Furthermore, the view direction is unfamiliar. We add the view option with the argument for view from top and congure the number of contour lines using the contour/number key and the line width using the thick style: x exp(x2 y 2 )1 0.50.1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

This is what we wanted to achieve. Note that contour gnuplot accepts options which have the key prex contour/. In this context, the prex is optional. Note that contour gnuplot is dierent from almost all other plot handlers of pgfplots with respect to one aspect: it relies on an external tool to compute coordinates whereas all other pgfplots plot handlers depend on TEX alone and do not need 3rd party tools. The nonlinear algorithm to compute contour lines is currently unavailable in pgfplots which is stressed by the name contour gnuplot. Consequently, you can only reproduce the example if you have gnuplot installed. pgfplots invokes the executable name gnuplot, i.e. the executable must be on your search path (the PATH environment variable must contain A it). And, more importantly, you have to tell L TEX that it is allowed to launch 3rd party executables while processing your .tex le. Typically, you have to add the argument -shell-escape to your TEX executable, i.e. one of latex -shell-escape texlename or pdflatex -shell-escape texlename or lualatex -shell-escape texlename or xelatex -shell-escape texlename . Note that it is occasionally named in a dierent way like -enable-write18. The interaction with gnuplot is controlled by means of temporary input- and output les.

0.2

0.2

0.2

3.5. SOLVING A REAL USECASE: FUNCTIONS OF TWO VARIABLES

37

Note that contour gnuplot and \addplot gnuplot are two ways to extend the built-in capabilities of pgfplots by means of gnuplots math library, although their use is optional.

3.5.5

Summary

We have sketched how to load a data table containing a sampled function of two variables, and we learned how to visualize such data as surface plot. We learned how to rotate the view, how to change the color shader of surface plots, how to enabled colorbars, and how to add scatter plots on top of surface plots. Furthermore, we encountered the rst contour plot as an example for how to sample a function of two variables by means of builtin methods of pgfplots. It should be stressed that pgfplots needs no external tool to generate such plots (except for contour gnuplot which is the only exception): every computer with a decent version of pgfplots can regenerate these plots. There is more to say about threedimensional axes, in particular regarding mesh/ordering, parametric plots, perhaps line plots in three dimensions or other plot types. Furthermore, there are some limitations regarding the z buffering, i.e. how pgfplots decides which parts of the gure are in front of others. These items can be read in Section 4.6 and its subsections. You might also be interested in styles to change the appearance of a threedimensional axis, compare Section 4.11.

Chapter 4

The Reference4.1A TEX-dialects: L TEX, ConTEXt, plain TEX

The starting point for pgfplots is an axis enviroment like axis or the logarithmic variants semilogxaxis, semilogyaxis or loglogaxis. A Each environment is available for L TEX, ConTEXt and plain TEX:A L TEX: \usepackage{pgfplots} \pgfplotsset{compat=1.9} and

\begin{tikzpicture} \begin{axis} ... \end{axis} \end{tikzpicture}

Here, the \pgfplotsset{compat=1.9} key should be set to at least version 1.3. Otherwise pgfplots assumes that your document has been generated years ago and attempts to run in backwards compatibility mode as good as it can.A A Since L TEX is the default for many people, this manual only shows L TEX examples. A full document sceleton can be found below this enumeration.

If you use latex / dvips or pdflatex, no further modications are necessary. For dvipdfm, you should use the \def\pgfsysdriver line as indicated above in the examples (see also Section 2.6.3).

4.2

The Axis-Environments

There is an axis environment for linear scaling, two for semi-logarithmic scaling and one for doublelogarithmic scaling. \begin{tikzpicture}[ options of tikz ] environment contents \end{tikzpicture} This is the graphics environment of Tik Z. It produces a single picture and encloses also every axis. Instead of using the environment version, there is also a shortcut command \tikz{ picture content } which can be used alternatively. \begin{axis}[ options ] environment contents \end{axis} The axis environment for normal plots with linear axis scaling. The every linear axis style key can be modied with\pgfplotsset{every linear axis/.append style={...}}

40

CHAPTER 4. THE REFERENCE to install styles specically for linear axes. These styles can contain both Tik Z- and pgfplots options.

to install styles specically for the case with xmode=log, ymode=normal. The logarithmic scaling means to apply the natural logarithm (base e) to each x coordinate. Furthermore, ticks will be typeset as 10 exponent , see Section 4.13 for more details. \begin{semilogyaxis}[ options ] environment contents \end{semilogyaxis} The axis environment for normal scaling of x and logarithmic scaling of y , The style every semilogy axis will be installed for each such plot. The same remarks as for semilogxaxis apply here as well. \begin{loglogaxis}[ options ] environment contents \end{loglogaxis} The axis environment for logarithmic scaling of both, x and y axes. As for the other axis possibilities, there is a style every loglog axis which is installed at the environments beginning. The same remarks as for semilogxaxis apply here as well. They are all equivalent to\begin{axis}[ xmode=log|normal, ymode=log|normal] ... \end{axis}

Inside of an axis environment, the \addplot command is the main user interface. It comes in two variants: \addplot for twodimensional visualization and \addplot3 for threedimensional visualization. \addplot[ options ] input data trailing path commands ;

This is the main plotting command, available within each axis environment. It can be used one or more times within an axis to add plots to the current axis. There is also an \addplot3 command which is described in Section 4.6. It reads point coordinates from one of the available input sources specied by input data , updates limits, remembers options for use in a legend (if any) and applies any necessary coordinate transformations (or logarithms). The options can be omitted in which case the next entry from the cycle list will be inserted as options . These keys characterize the plots type like linear interpolation with sharp plot, smooth plot, constant interpolation with const plot, bar plot, mesh plots, surface plots or whatever and dene colors, markers and line specications1 . Plot variants like error bars, the number of samples or a sample domain can also be congured in options . The input data is one of several coordinate input tools which are described in more detail below. Finally, if \addplot successfully processed all coordinates from input data , it generates Tik Z paths to realize the drawing operations. Any trailing path commands are appended to the nal drawing command, allowing to continue the Tik Z path (from the last plot coordinate). Some more details: The style /pgfplots/every axis plot will be installed at the beginning of options . That means you can use\pgfplotsset{every axis plot/.append style={...}}

to add options to all your plots - maybe to set line widths to thick. Furthermore, if you have more than one plot inside of an axis, you can also use\pgfplotsset{every axis plot no 3/.append style={...}}

to modify options for the plot with number 3 only. The rst plot in an axis has number 0. The options are remembered for the legend. They are available as current plot style as long as the path is not yet nished or in associated error bars. See Subsection 4.7 for a list of available markers and line styles. For log plots, pgfplots will compute the natural logarithm log() numerically using a oating point unit developed for this purpose2 . For example, the following numbers are valid input to \addplot.1 In version 1.2.2 and earlier, there was an explicit distinction between behaviour options like error bars, domain, number of samples etc. and style options like color, line width, markers etc. This distinction is obsolete now, simply collect everything into options . 2 This oating point unit is available as Tik Z library as part of Tik Z.

You can represent arbitrarily small or very large numbers as long as its logarithm can be represented as a TEX-length (up to about 16384). Of course, any coordinate x 0 is not possible since the logarithm of a non-positive number is not dened. Such coordinates will be skipped automatically (using the initial conguration unbounded coords=discard). For normal (nonlogarithmic) axes, pgfplots applies oating point arithmetics to support large or small numbers like 0.00000001234 or 1.234 1024 . Its number range is much larger than TEXs native support for numbers. The relative precision is between 4 and 7 signicant decimal digits for the mantissa. As soon as the axes limits are completely known, pgfplots applies a transformation which maps these oating point numbers into TEX-precision using transformations

Tx (x) = 10sx x ax and Ty (y ) = 10sy y ay and (for 3D plots) Tz (y ) = 10sz z az with properly chosen integers sx , sy , sz Z and shifts ax , ay , az R. Section 4.26 contains a description of disabledatascaling and provides more details about the transformation. Some of the coordinate input routines use the powerful \pgfmathparse feature of pgf to read their coordinates, among them plot coordinates, plot expression and plot table. This allows to use mathematical expressions as coordinates which will be evaluated using the oating point routines (this applies to logarithmic and linear scales). pgfplots automatically computes missing axis limits. The automatic computation of axis limits works as follows:

1. Every coordinate will be checked. Care has been taken to avoid TEXs limited numerical capabilities. 2. Since more than one \addplot command may be used inside of \begin{axis}...\end{axis}, all drawing commands will be postponed until \end{axis}. \addplot+[ options ] ...; Does the same like \addplot[ options ] ...; except that options are appended to the arguments which would have been taken for \addplot ... (the element of the default list). Thus, you can combine cycle list and options . 1 1

Controls how empty lines in the input coordinate stream are to be interpreted. You should ensure that you have \pgfplotsset{compat=1.4} or newer in your preamble and leave this key at its default empty line=auto. Empty lines can occur between the coordinates of \addplot coordinates or successive rows of the data le input routines \addplot table (and \addplot file). The choice auto checks if the current plot type is mesh or surf. If so, it uses scanline. If the current plot type is some other plot type (like a standard line plot), it uses jump. Note that the value auto for non-mesh plots results in none if compat=1.3 or older is used. In other words: you have to write \pgfplotsset{compat=1.4} or newer to let pgfplots interpret empty lines as jump in standard line plots:Ignored: compat=1.32 1.5 1 0.5 0 0 0.5 1 1.5 2 2 1 .5 1 0 .5 0 0 0.5 1 1.5 2

The choice scanline is only useful for mesh and surf: it is used to decode a matrix from a coordinate stream. If an empty line occurs once every N data points, the scanline length is N . This information, together with mesh/ordering and the total number of points, allows to deduce the matrix size. However, the distance between empty lines has to be consistent: if the rst two empty lines have a distance of 2 and the next comes after 5, pgfplots will ignore the information and will expect explicit matrix sizes using mesh/rows and/or mesh/cols. The choice scanline is ignored if mesh input=patches. It has no eect for other plot types.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT The choice none will silently discard any empty line in the input stream. The choice jump tells pgfplots to generate a jump.

0 0 0.2 0.4 0.6 0.8 1

You should only use this input format if you have short diagrams and you want to provide mathematical expressions for each of the involved coordinates. Any data plots are typically easier to handle using a table format and \addplot table. The coordinates can be numbers, but they can also contain mathematical expressions like sin(0.5) or \h*8 (assuming you dened \h somewhere). However, expressions which involve round braces need to be encapsulated in a further set of curly braces, for example ({sin(0.5)},{cos(0.1)}). You can also supply error coordinates (reliability bounds) if you are interested in error bars. Simply append the error coordinates with +- ( ex,ey ) (or +- ( ex,ey,ez )) to the associated coordinate:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

These error coordinates are only used in case of error bars, see Section 4.12. You will also need to congure whether these values denote absolute or relative errors. The coordinates as such can be numbers as +5, -1.2345e3, 35.0e2, 0.00000123 or 1e2345e-8. They are not limited to TEXs precision.

46

CHAPTER 4. THE REFERENCE Furthermore, coordinates allows to dene meta data for each coordinate. The interpretation of meta data depends on the visualization technique: for scatter plots, meta data can be used to dene colors or style associations for every point (see page 100 for an example). Meta data (if any) must be provided after the coordinates and after error bar bounds (if any) in square brackets: 106 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Please refer to the documentation of point meta on page 179 for more information about per point meta data. The coordinate stream can contain empty lines to tell pgfplots that the function has jumps. To use it, simply insert an empty line (and ensure that you have \pgfplotsset{compat=1.4} or newer in your preamble). See the documentation of empty line for details. /pgfplots/plot coordinates/math parser=true|false (initially true) Allows to turn o support for mathematical expressions in every coordinate inside of plot coordinates. This might be necessary if coordinates are not in numerical form (or if youd like to improve speed). It is necessary to disable plot coordinates/math parser if you use some sort of symbolic transformations (i.e. text coordinates).

Inline table may be convenient together with \\ and row sep=\\, see below for more information. Alternatively, you can load the table once into an internal structure and use it multiple times3 :\pgfplotstableread{datafile.dat}\loadedtable % ... \addplot table[x=dof,y=L2] {\loadedtable}; ... \addplot table[x=dof,y=Lmax] {\loadedtable}; ... use any custom name in place of \loadedtable

I am not really sure how much time can be saved, but it works anyway. The \pgfplotstableread command is documented in all detail in the manual for PgfplotsTable. As a rule of thumb, decide as follows: 2. If tables contain more than 200 data points (rows), you should always use le input (and reload if necessary). Occasionally, it might be handy to load a table, apply manual preparation steps (for example \pgfplotstabletranspose) and plot the result tables afterwards. If you do prefer to access columns by column indices instead of column names (or your tables do not have column names), you can also use\addplot table[x index=2,y index=3] {datafile.dat}; \addplot table[x=dof,y index=2] {datafile.dat};

1. If tables contain few rows and many columns, the \macro framework will be more ecient.

Summary and remarks:

Use \addplot table[x={ column name },y={ column name }] to access column names. Those names are case sensitive and need to exist. Use \addplot table[x index={ column index },y index={ column index }] to access column indices. Indexing starts with 0. You may also use an index for x and a column name for y . Use \addplot table[x expr=\coordindex,y={ column name }] to plot the coordinate index versus some y data.earlier versions, there was an addition keyword from before the argument like \addplot table from {\loadedtable}. This keyword is still accepted, but no longer required.3 In

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CHAPTER 4. THE REFERENCE

Use \addplot table[header=false] { le name } if your input le has no column names. Otherwise, the rst non-comment line is checked for column names: if all entries are numbers, they are treated as numerical data; if one of them is not a number, all are treated as column names. It is possible to read error coordinates from tables as well. Simply add options x error, y error or x error index/y error index to source columns . See Section 4.12 for details about error bars. It is possible to read per point meta data (usable in scatter src, see page 98) as has been discussed for plot coordinates and plot file above. The meta data column can be provided using the meta key (or the meta index key). Use \addplot table[ source columns ] { \macro } to use a preread table. Tables can be read using\pgfplotstableread{datafile.dat}\macroname.

If you like, you can insert the optional keyword from before \macroname. The accepted input format of tables is as follows:

Rows are separated by new line characters. Alternatively, you can use row sep=\\ which enables \\ as row separator. This might become necessary for inline table data, more precisely: if newline characters have been converted to white spaces by TEXs character processing before pgfplots had a chance to see them. This happens if inline tables are provided inside of macros. Use row sep=\\ and separate the rows by \\ if you experience such problems. Columns are usually separated by white spaces (at least one tab or space). If you need other column separation characters, you can use the col sep=space|tab|comma|colon|semicolon|braces|&|ampersand option documented in all detail in the manual for PgfplotsTable which is part of pgfplots. Any line starting with # or % is ignored. The rst line will be checked if it contains numerical data. If there is a column in the rst line which is no number, the complete line is considered to be a header which contains column names. Otherwise it belongs to the numerical data and you need to access column indices instead of names. There is future support for a second header line which must start with $flags . Currently, such a line is ignored. It may be used to provide number formatting hints like precision and number format if those tables shall be typeset using \pgfplotstabletypeset (see the manual for PgfplotsTable). The accepted number format is the same as for plot coordinates, see above. If you omit column selectors, the default is to plot the rst column against the second. That means plot table does exactly the same job as plot file for this case. If you need unbalanced columns, simply use nan as empty cell placeholder. These coordinates will be skipped in plots. It is also possible to use mathematical expressions together with plot table. This is documented in all detail in Section 4.3.4, but the key idea is to use one of x expr, y expr, z expr or meta expr as in plot table[x expr=\thisrow{maxlevel}+3,y=L2]. The PgfplotsTable package coming with pgfplots has a the feature Postprocessing Data in New Columns (see its manual). This allows to compute new columns based on existing data. One of these features is create col/linear regression (described in Section 4.25). You can invoke all the create col/ key name features directly in \addplot table using \addplot table[x={create col/ key name = arguments }]. In this case, a new column will be created using the functionality of key name . This column generation is described in all detail in PgfplotsTable. Finally, the resulting data is available as x coordinate (the same holds for y= or z=). One application (with several examples how to use this syntax) is line tting with create col/linear regression, see Section 4.25 for details.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

49

The table can contain empty lines to tell pgfplots that the function has jumps. To use it, simply insert an empty line (and ensure that you have \pgfplotsset{compat=1.4} or newer in your preamble). See the documentation of empty line for details. Technical note: every opened le will be protocolled into your log le.

Keys To Congure Table Input

The following list of keys allow dierent methods to select input data or dierent input formats. Note that the common prex table/ can be omitted if these keys are set after \addplot table[ options ]. The /pgfplots/ prex can always be omitted when used in a pgfplots method. /pgfplots/table/header=true|false Allows to disable header identication for plot table. See above. /pgfplots/table/x={ column name } /pgfplots/table/y={ column name } /pgfplots/table/z={ column name } /pgfplots/table/x index={ column index } /pgfplots/table/y index={ column index } /pgfplots/table/z index={ column index } These keys dene the sources for plot table. If both column names and column indices are given, column names are preferred. Column indexing starts with 0. The initial setting is to use x index=0 and y index=1. Please note that column aliases will be considered if unknown column names are used. Please refer to the manual of PgfplotsTable which comes with this package. /pgfplots/table/x expr={ expression } /pgfplots/table/y expr={ expression } /pgfplots/table/z expr={ expression } /pgfplots/table/meta expr={ expression } These keys allow to combine the mathematical expression parser with le input. They are listed here to complete the list of table keys, but they are described in all detail in Section 4.3.4. The key idea is to provide an expression which depends on table data (possibly on all columns in one row). Only data within the same row can be used where columns are referenced with \thisrow{ column name } or \thisrowno{ column index }. Please refer to Section 4.3.4 for details. /pgfplots/table/x error={ column name } /pgfplots/table/y error={ column name } /pgfplots/table/z error={ column name } /pgfplots/table/x error index={ column index } /pgfplots/table/y error index={ column index } /pgfplots/table/z error index={ column index } /pgfplots/table/x error expr={ math expression } /pgfplots/table/y error expr={ math expression } /pgfplots/table/z error expr={ math expression } These keys dene input sources for error bars with explicit error values. The x error method provides an input column name (or alias), the x error index method provides input column indices and x error expr works just as table/x expr: it allows arbitrary mathematical expressions which may depend on any number of table columns using \thisrow{ col name }. Please see Section 4.12 for details about the usage of error bars. /pgfplots/table/x /pgfplots/table/y /pgfplots/table/z /pgfplots/table/x /pgfplots/table/y error error error error error plus={ column name } plus={ column name } plus={ column name } plus index={ column index } plus index={ column index } (initially true)

CHAPTER 4. THE REFERENCE

These keys dene input sources for error bars with asymmetric error values, i.e. dierent values for upper and lower bounds. They are to be used in the same way as x error. In fact, x error is just a style which sets both x error plus and x error minus to the same value. Please see Section 4.12 for details about the usage of error bars. /pgfplots/table/meta={ column name } /pgfplots/table/meta index={ column index } These keys dene input sources for per point meta data. Please see page 98 for details about meta data or the documentation for plot coordinates and plot file for further information. /pgfplots/table/row sep=newline|\\ Congures the character to separate rows. (initially newline)

The choice newline uses the end of line as it appears in the table data (i.e. the input le or any inline table data). The choice \\ uses \\ to indicate the end of a row. Note that newline for inline table data is fragile: you cant provide such data inside of TEX macros (this does not apply to input les). Whenever you experience problems, proceed as follows: 1. First possibility: call \pgfplotstableread{ data }\yourmacro outside of any macro declaration. 2. Use row sep=\\. The same applies if you experience problems with inline data and special col sep choices (like col sep=tab). The reasons for such problems is that TEX scans the macro bodies and replaces newlines by white spaces. It does other substitutions of this sort as well, and these substitutions cant be undone (maybe not even found). /pgfplots/table/col sep=space|tab|comma|semicolon|colon|braces|&|ampersand (initially space)

Allows to choose column separators for plot table. Please refer to the manual of PgfplotsTable which comes with this package for details about col sep. (initially auto)

/pgfplots/table/read completely={ auto,true,false }

Allows to customize \addplot table{ le name } such that it always reads the entire table into memory. This key has just one purpose, namely to create postprocessing columns on-the-y and to plot those columns afterwards. This lazy evaluation which creates missing columns on-the-y is documented in the PgfplotsTable manual (in section Postprocessing Data in New Columns). The initial conguration auto checks whether one of the keys table/x, table/y, table/z or table/meta contains a create on use column. If so, it enables read completely, otherwise it prefers to load the le in the normal way. Attention: Usually, \addplot table only picks required entries, requiring linear runtime complexity. As soon as read completely is activated, tables are loaded completely into memory. Due to datastruc-

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

51

tures issues (macro append runtime), the runtime complexity for read completely is O(N 2 ) where N is the number of rows. Thus: use this feature only for small tables4 . /pgfplots/table/ignore chars={ comma-separated-list } (initially empty)

Allows to silently remove a set of single characters from input les. The characters are separated by commas. The documentation for this command, including cases like \%,\#,\ or binary character codes like \^^ff can be found in the manual for PgfplotsTable. This setting applies to \addplot file as well. /pgfplots/table/white space chars={ comma-separated-list } (initially empty)

Allows to dene a list of single characters which are actually treated like white spaces (in addition to tabs and spaces). Please refer to the manual of PgfplotsTable for details. This setting applies to \addplot file as well. /pgfplots/table/comment chars={ comma-separated-list } (initially empty)

Allows to add one or more additional comment characters. Each of these characters has a similar eect as the # character, i.e. all following characters of that particular input line are skipped. For example, comment chars=! uses ! as additional comment character (which allows to parse Touchstone les). Please refer to the manual of PgfplotsTable for details. /pgfplots/table/skip first n={ integer } Allows to skip the rst integer lines of an input le. The lines will not be processed. Please refer to the manual of PgfplotsTable for details. (initially 0)

4.3.3

Computing Coordinates with Mathematical Expressions

This input method allows to provide mathematical expressions which will be sampled. But unlike plot gnuplot, the expressions are evaluated using the math parser of pgf, no external program is required. Plot expression samples x from the interval [a, b] where a and b are specied with the domain key. The number of samples can be congured with samples= N as for plot gnuplot.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Please note that pgfs math parser uses degrees for trigonometric functions:remark might be deprecated; many of the slow routines have been optimized in the meantime to have at least pseudolinear runtime.4 This

1 0 100 200 300

If you want to use radians, use 1

to convert the radians to degrees. The plot expression parser also accepts some more options like samples at={ coordinate list } or domain= rst : last which are described below. Remarks 1. What really goes on is a loop which assigns the current sample coordinate to the macro \x. pgfplots denes a math constant x which always has the same value as \x. In short: it is the same whether you write \x or just x inside of math expressions. The variable name can be customized using variable=\t (the backslash is necessary!). Then, t will be the same as \t. 2. The complete set of math expressions can be found in the pgf manual. The most important mathematical operations are +, -, *, /, abs, round, floor, mod, <, >, max, min, sin, cos, tan, deg (conversion from radians to degrees), rad (conversion from degrees to radians), atan, asin, acos, cot, sec, cosec, exp, ln, sqrt, the constants pi and e, ^ (power operation), factorial5 , rand (random between 1 and 1), rnd (random between 0 and 1), number format conversions hex, Hex, oct, bin and some more. The math parser has been written by Mark Wibrow and Till Tantau [5], the FPU routines have been developed as part of pgfplots. The documentation for both parts can be found in [5]. Please note, however, that trigonometric functions are dened in degrees. The character ^ is used for exponentiation (not ** as in gnuplot). 3. If the x axis is logarithmic, samples will be drawn logarithmically. 4. Please note that plot expression does not allow separate per point meta data (color data). You can, of course, use point meta=f(x) or point meta=x. About the precision and number range: Starting with version 1.2, plot expression uses a oating point unit. The FPU provides the full data range of scientic computing with a relative precision between 104 and 106 . The /pgf/fpu key provides some more details.5 Starting

with pgf versions newer than 2.00, you can use the postx operator ! instead of factorial.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

53

In case the fpu does not provide the desired mathematical function or is too slow6 , you should consider using the plot gnuplot method which invokes the external, freely available program gnuplot as desktop calculator.1 x2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

A variant of \addplot expression which allows to provide dierent coordinate expressions for the x and y coordinates. This can be used to generate parametrized plots. Please note that \addplot (x,x^2) is equivalent to \addplot expression {x^2}. Note further that since the complete point expression is surrounded by round braces, round braces for either x expression or y expression need special attention. You will need to introduce curly braces additionally to allow round braces: \addplot ({ x expr }, { y expr }, { z expr }); /pgfplots/domain= x1 : x26 Or

(initially [-5:5])

in case you nd a bug. . .

54 /pgfplots/y domain= y1 : y2 /pgfplots/domain y= y1 : y2

CHAPTER 4. THE REFERENCE

Sets the functions domain(s) for plot expression and plot gnuplot. Two dimensional plot expressions are dened as functions f : [x1 , x2 ] R and x1 and x2 are set with domain. Three dimensional plot expressions use functions f : [x1 , x2 ] [y1 , y2 ] R and y1 and y2 are set with y domain. If y domain is empty, [y1 , y2 ] = [x1 , x2 ] is assumed for three dimensional plots (see page 112 for details about three dimensional plot expressions). The keys y domain and domain y are the same. The domain key wont be used if samples at is specied; samples at has higher precedence. Please note that domain is not necessarily the same as the axis limits (which are congured with the xmin/xmax options). The domain keys are only relevant for gnuplot and plot expression. In case youd like to plot only a subset of other coordinate input routines, consider using the coordinate lter restrict x to domain. Remark for Tik Z-users: /pgfplots/domain and /tikz/domain are independent options. Please prefer the pgfplots variant (i.e. provide domain to an axis, \pgfplotsset or a plot command). Since older versions also accepted something like \begin{tikzpicture}[domain=. . . ], this syntax is also accepted as long as no pgfplots domain key is set. /pgfplots/samples={ number } /pgfplots/samples y={ number } (initially 25)

Sets the number of sample points for plot expression and plot gnuplot. The samples key denes the number of samples used for line plots while the samples y key is used for mesh plots (three dimensional visualisation, see page 112 for details). If samples y is not set explicitly, it uses the value of samples. The samples key wont be used if samples at is specied; samples at has higher precedence. The same special treatment of /tikz/samples and /pgfplots/samples as for the domain key applies here. See above for details. /pgfplots/samples at={ coordinate list } Sets the x coordinates for plot expression explicitly. This overrides domain and samples. The coordinate list is a \foreach expression, that means it can contain a simple list of coordinates (commaseparated), but also complex ... expressions like7\pgfplotsset{samples at={5e-5,7e-5,10e-5,12e-5}} \pgfplotsset{samples at={-5,-4.5,...,5}} \pgfplotsset{samples at={-5,-3,-1,-0.5,0,...,5}}

The same special treatment of /tikz/samples at and /pgfplots/samples at as for the domain key applies here. See above for details. Attention: samples at overrides domain, even if domain has been set after samples at! samples at={} to clear coordinate list and re-activate domain. /pgfplots/variable={ variable name } /pgfplots/variable y={ variable name } Use

(initially x) (initially y)

Denes the variables names which will be sampled in domain (with variable) and in domain y (with variable y). The same variables are used for parametric and for non-parametric plots. Use variable=t to change them if you like (for gnuplot, there is such a distinction; see parametric/var 1d). Technical remark: Tik Z also uses the variable key. However, it expects a macro name, i.e. \x instead of just x. Both possibilities are accepted here.7 Unfortunately, the ... is somewhat restrictive when it comes to extended accuracy. So, if you have particularly small or large numbers (or a small distance), you have to provide a commaseparated list (or use the domain key).

Besides x expr, there are keys y expr, z expr and meta expr where the latter allows to provide point meta data (which is used as scatter src or color data for surface plots etc.). Inside of expression , the following macros can be used to access numerical data cells inside of the input le:

56 \thisrow{ column name }

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Yields the value of the column designated by column name . There is no limit on the number of columns which can be part of a mathematical expression, but only values inside of the currently processed table row can be used. It is possible to provide column aliases for column name as described in the manual of PgfplotsTable. The argument column name has to denote either an existing column or one for which a column alias exists (see the manual of PgfplotsTable). If it cant be resolved, the math parser yields an Unknown function error message. \thisrowno{ column index } Similar to \thisrow, this command yields the value of the column with index column index (starting with 0). \coordindex Yields the current index of the table row (starting with 0). This does not count header or comment lines. \lineno Yields the current line number (starting with 0). This does also count header and comment lines. If x index, x and x expr (or the corresponding keys for y, z or meta) are combined, this is how they interact: 1. Column access via x has higher precedence than index access via x index. 2. Even if x expr is provided, the values of x index and x are still checked. Any value found using column name access or column index access is made available as \columnx (or \columny, \columnz, \columnmeta, resp.). However, the result of x expr is used as plot coordinate. This allows to access the cell values identied by x or x index using the pointer \columnx. I am not sure if this yields any advantage, but it is possible nevertheless. If in doubt, prefer using \thisrow{ column name }. Attention: If your table has less than two rows, you may need to set x index={},y index={} explicitly. This is a consequence of the fact that column name/index access is still applied even if an expression is provided.

4.3.5

Computing Coordinates with Mathematical Expressions (gnuplot)

\addplot gnuplot [ further options ]{ gnuplot code }; \addplot[ options ] gnuplot [ further options ]{ gnuplot code } trailing path commands ; \addplot3 . . . In contrast to plot expression, the plot gnuplot command8 employs the external program gnuplot to compute coordinates. The resulting coordinates are written to a text le which will be plotted with plot file. pgf checks whether coordinates need to be re-generated and calls gnuplot whenever necessary (this is usually the case if you change the number of samples, the argument to plot gnuplot or the plotted domain9 ). The dierences between plot expression and plot gnuplot are: plot expression does not require any external programs and requires no additional command line options. plot expression does not produce a lot of temporary les. plot gnuplot uses radians for trigonometric functions while plot expression has degrees. plot gnuplot is faster.that plot gnuplot is actually a re-implementation of the plotfunction method known from pgf. It also invokes pgf basic layer commands. 9 Please note that pgfplots produces slightly dierent les than Tik Z when used with plot gnuplot (it congures high precision output). You should use dierent id for pgfplots and Tik Z to avoid conicts in such a case.8 Note

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

plot gnuplot has a larger mathematical library.

57

plot gnuplot has a higher accuracy. However, starting with version 1.2, this is no longer a great problem. The new oating point unit for TEX provides reasonable accuracy and the same data range as gnuplot.

Since system calls are a potential danger, they need to be enabled explicitly using command line options, for examplepdflatex -shell-escape filename.tex.

Sometimes it is called shell-escape or enable-write18. Sometimes one needs two hyphens that all depends on your TEX distribution. 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

103 102 101 100 0 2 4 6 8 10

The options determine the appearance of the plotted function; these parameters also aect the legend. There is also a set of options which are specic to the gnuplot interface. These options are described in all detail in [5, section 18.6]. A short summary is shown below. Some remarks: The independent variable for one-dimensional plots can be changed with the variable option, just as for plot expression. Similarly, the second variable for two dimensional plots can be changed with variable y. For parametric plots, the variable names need to be adjusted with parametric/var 1d and parametric/var 2d (since gnuplot uses t and u,v as initial values for parametric plots). Please note that plot gnuplot does not allow separate per point meta data (color data for each coordinate). You can, however, use point meta=f(x) or point meta=x. The generated output le name can be customized with id, see below.

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Enables or disables automatic translation of the exponentiation operator ^ to **.

This features allows to use ^ in plot gnuplot instead of gnuplots **. /pgfplots/parametric=true|false (initially false)

Set this to true if youd like to use parametric plots with gnuplot. Parametric plots use a comma separated list of expressions to make up x(t), y (t) for a line plot or x(u, v ), y (u, v ) z (u, v ) for a mesh plot (refer to the gnuplot manual for more information about its input methods for parametric plots). (initially t) (initially u,v)

Allows to change the dummy variables used by parametric gnuplot plots. The initial setting is the one of gnuplot: to use the dummy varialbe t for parametric line plots and u,v for parametric mesh plots. These keys are quite the same as variable and variable y, only for parametric plots. If you like to change variables for non-parametric plots, use variable and/or variable y. In case you dont want the distinction between parametric and non-parametric plots, use \pgfplotsset{parametric/var 1d=,parametric/var 2d=}. /tikz/id={ unique string identier } A unique identier for the current plot. It is used to generate temporary lenames for gnuplot output. /tikz/prefix={ le name prex } A common path prex for temporary lenames (see [5, section 18.6] for details). /tikz/raw gnuplot Disables the use of samples and domain. (no value)

4.3.6

Computing Coordinates with External Programs (shell)

In contrast to plot gnuplot, the plot shell command allows execution of arbitrary shell commands to compute coordinates. The resulting coordinates are written to a text le which will be plotted with plot file. pgf checks whether coordinates need to be re-generated and executes the shell commands whenever necessary. Since system calls are a potential danger, they need to be enabled explicitly using command line options, for examplepdflatex -shell-escape filename.tex.

Sometimes it is called shell-escape or enable-write18. Sometimes one needs two slashes that all depends on your TEX distribution.

The options determine the appearance of the plotted function; these parameters also aect the legend. There is also a set of options which are specic to the gnuplot and the shell interface. These options are described in all detail in [5, section 19.6]. A short summary is shown below. /tikz/id={ unique string identier } A unique identier for the current plot. It is used to generate temporary lenames for shell output. /tikz/prefix={ le name prex } A common path prex for temporary lenames (see [5, section 19.6] for details).

4.3.7

Using External Graphics as Plot Sources

\addplot graphics { le name }; \addplot[ options ] graphics { le name } trailing path commands ; \addplot3 . . . This plot type allows to extend the plotting capabilities of pgfplots beyond its own limitations. The idea is to generate the graphics as such (for example, a contour plot, a complicated shaded surface10 or a large point cluster) with an external program like Matlab () or gnuplot. The graphics, however, should not contain an axis or descriptions. Then, we use \includegraphics and a pgfplots axis which ts exactly on top of the imported graphics. Of course, one could do this manually by providing proper scales and such. The operation plot graphics is intended so simplify this process. However the main diculty is to get images with correct bounding box. Typically, you will have to adjust bounding boxes manually. Lets start with an example: Suppose we use, for example, matlab to generate a surface plot like[X,Y] = meshgrid( linspace(-3,3,500) ); surf( X,Y, exp(-(X - Y).^2 - X.^2 ) ); shading flat; view(0,90); axis off; print -dpng external110 See

also Section 4.6.6 for an overview of pgfplots methods to draw shaded surfaces.

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CHAPTER 4. THE REFERENCE which is then found in external1.png. The surf command of Matlab generates the surface, the following commands disable the axis descriptions, initialise the desired view and export it. Viewing the image in any image tool, we see a lot of white space around the surface Matlab has a particular weakness in producing tight bounding boxes, as far as I know. Well, no problem: use your favorite image editor and crop the image (most image editors can do this automatically). We could use the free ImageMagick command convert -trim external1.png external1.png to get a tight bounding box. Then, we use% Preamble: \pgfplotsset{width=7cm,compat=1.9}

to load the graphics11 just as if we would have drawn it with pgfplots. The axis on top simply tells pgfplots to draw the axis on top of any plots (see its description). Please note that pgfplots oers support for smaller surface plots as well which might be an option unless the number of samples is too large. See Section 4.6.6 for details. However, external programs have the following advantages here: they are faster, allow more complexity and provide real z buering which is currently only simulated by pgfplots. Thus, it may help to consider plot graphics for complicated surface plots. Our rst test was successful and not dicult at all because graphics programs can automatically compute the bounding box. There are a couple of free tools available which can compute tight bounding boxes for .eps or .pdf graphics: 1. The free vector graphics program inkscape can help here. Its feature File Document Properties: Fit page to selection computes a tight bounding box around every picture element. However, some images may contain a rectangular path which is as large as the bounding box (Matlab () computes such .eps images). In this case, use the Ungroup method (context menu of inkscape) as often as necessary and remove such a path. Finally, save as .eps. However, inkscape appears to have problems with postscript fonts it substitutes them. This doesnt pose problems in this application because fonts shouldnt be part of such images the descriptions will be drawn by pgfplots. 2. The tool pdfcrop removes surrounding whitespace in .pdf images and produces quite good bounding boxes. Adjusting bounding boxes manually In case you dont have tools at hand to provide correct bounding boxes, you can still use TEX to set the bounding box manually. Some viewers like gv provide access to lowlevel image coordinates. The idea is to determine the number of units which need to be removed and communicate these units to \includegraphics. I am aware of the following methods to determine bounding boxes manually: inkscape I am pretty sure that inkscape can do it. gv The ghost script viewer gv always shows the postscript units under the mouse cursor.11 Please

note that I dont have a Matlab license, so I used gnuplot to produce an equivalent replacement graphics.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

61

gimp The graphics program gimp usually shows the cursor position in pixels, but it can be congured to display postscript points (pt) instead. Lets follow this approach in a further example. We use gnuplot to draw a (relatively stupid) example data set. The gnuplot scriptset samples 30000 set parametric unset border unset xtics unset ytics set output "external2.eps" set terminal postscript eps color plot [t=0:1] rand(0),rand(0) with dots notitle lw 5

generates external2.eps with a uniform random sample of size 30000. As before, we import this scatter plot into pgfplots using plot graphics. Again, the bounding box is too large, so we need to adjust it (gnuplot can do this automatically, but we do it anyway to explain the mechanisms): Using gv, I determined that the bounding box needs to be shifted 12 units to the left and 9 down. Furthermore, the right end is 12 units too far o and the top area has about 8 units space wasted. This can be provided to the trim option of \includegraphics, and we use clip to clip the rest away: Graphics Import 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0 0 0.2 0.4 0.6 0.8 1

So, plot graphics takes a graphics le along with options which can be passed to \includegraphics. Furthermore, it provides the information how to embed the graphics into an axis. The axis can contain any other \addplot command as well and will be resized properly. Details about plot graphics: The loaded graphics le is drawn with \node[/pgfplots/plot graphics/node] {\includegraphics[ options ]{ le name }}; where the node style is a congurable style. The node is placed at the coordinate designated by xmin, ymin. The options are any arguments provided to the includegraphics key (see below) and width and height determined such that the graphics ts exactly into the rectangle denoted by the xmin, ymin and xmax, ymax coordinates. The scaling will thus ignore the aspect ratio of the external image and prefer the one used by pgfplots. You will need to provide width and height to the pgfplots axis to change its scaling. Use the scale only axis key in such a case. Legends in plot graphics: A legend for plot graphics uses the current plot handler and the current plot mark:

0 0 0.2 0.4 0.6 0.8 1

Keys To Congure Plot Graphics

The following list of keys congure \addplot graphics. Note that the common prex plot graphics/ can be omitted if these keys are set after \addplot graphics[ options ]. The /pgfplots/ prex can always be omitted when used in a pgfplots method. /pgfplots/plot /pgfplots/plot /pgfplots/plot /pgfplots/plot /pgfplots/plot /pgfplots/plot graphics/xmin={ graphics/ymin={ graphics/zmin={ graphics/xmax={ graphics/ymax={ graphics/zmax={ coordinate coordinate coordinate coordinate coordinate coordinate } } } } } }

These keys are required for plot graphics and provide information about the external data range. The graphics will be squeezed between these coordinates. The arguments are axis coordinates; they are only useful if you provide each of them. Alternatively, you can also use the plot graphics/points feature to provide the external data range, see below. /pgfplots/plot graphics/points={ list of coordinates } (initially empty)

This key also allows to provide the external data range. It constitutes an alternative to plot graphics/xmin (and its variants): simply provide at least two coordinates in list of coordinates . Their bounding box is used to determine the external data range, and the graphics is squeezed between these coordinates. The example from above can be written equivalently as Graphics Import 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0 0 0.2 0.4 0.6 0.8 1

The list of coordinates is a sequence of the form (x,y) for twodimensional plots and (x,y,z) for threedimensional ones, the ordering is irrelevant. The single elements are separated by white space.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT It is possible to mix plot graphics/xmin and variants with plot graphics/points.

63

The plot graphics/points key has further functionality for inclusion of threedimensional graphics which is discussed at the end of this section (on page 63). Here is a short reference on the accepted syntax for threedimensional plot graphics: in addition to the (x,y,z) syntax, you can provide arguments of the form (x,y,z) => (X,Y). Here, the rst (threedimensional) coordinate is a logical coordinate and the second (twodimensional) coordinate denotes the coordinates of the very same point, but inside of the included image (relative to the lower left corner of the image). Applications and examples for this syntax can be found in the section for threedimensional plot graphics (see page 63). /pgfplots/plot graphics/includegraphics={ options } A list of options which will be passed asis to \includegraphics. Interesting options include the trim= left bottom right top key which reduces the bounding box and clip which discards everything outside of the bounding box. The scaling options wont have any eect, they will be overwritten by pgfplots. /pgfplots/plot graphics/includegraphics cmd={ \macro } Allows to use a dierent graphics routine. A possible choice could be \pgfimage. The macro should accept the width and height arguments (in brackets) and the le name as rst argument. (style, no value) A predened style used for the Tik Z node containing the graphics. The predened value is\pgfplotsset{ plot graphics/node/.style={ transform shape, inner sep=0pt, outer sep=0pt, every node/.style={}, anchor=south west, at={(0pt,0pt)}, rectangle } }

(initially \includegraphics)

/pgfplots/plot graphics/node

/pgfplots/plot graphics This key belongs to the public lowlevel plotting interface. You wont need it in most cases.

(no value)

This key is similar to sharp plot or smooth or const plot: it installs a lowlevel plothandler which expects exactly two points: the lower left corner and the upper right one. The graphics will be drawn between them. The graphics le name is expected as value of the /pgfplots/plot graphics/src key. The other keys described above need to be set correctly (excluding the limits, these are ignored at this level of abstraction). This key can be used independently of an axis. /pgfplots/plot graphics/lowlevel draw={ width }{ height } A lowlevel interface for plot graphics which actually invokes \includegraphics. But there is no magic involved: the command is simply expected to draw a box of dimensions width height . The coordinate system has already been shifted correctly. The initial conguration is \includegraphics[ value of plot graphics/includegraphics ,width=#1,height=#2] { value of plot graphics/src }. Thus, you can tweak plot graphics to place any TEX box of the desired dimensions into an axis between the provided minimum and maximum coordinates. It is not necessary to make use of the graphics le name or the options in the includegraphics key if you overwrite this lowlevel interface with plot graphics/lowlevel draw/.code 2 args={ code which depends on #1 and #2 }.

Support for External Three-Dimensional Graphics

pgfplots oers several visualization techniques for three dimensional graphics. Nevertheless, complex visualizations or specialized applications are beyond the scope of pgfplots and you might want to use other tools to generate such gures.

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Figure 4.1: Using Matlab to extract image coordinates (left) and Gimp to measure distances (right). The plot graphics tool of pgfplots allows to include threedimensional external graphics: it generates a threedimensional axis on its own. The idea is to provide a graphics (without descriptions) and use pgfplots to overlay a threedimensional axis automatically. This allows to maintain document consistency (making it unnecessary to use dierent programs within the same document). You are probably wondering how this is possible. Well, it needs more user input than twodimensional external graphics. The cost to include external three dimensional images into pgfplots is essentially control of a graphics program like gimp: you need to identify the 3D coordinates of a couple of points in your image. pgfplots will then squeeze the graphics correctly, and it recongures the axis to ensure a correct display of the result. Matlab versus other tools: Although this section is based on Matlab images, the technique to import threedimensional graphics is independent of Matlab. Thus, if you have a dierent tool, you need to read all that follows. However, users of Matlab can use a simplied export mechanism which has been contributed by J urnjakob Dugge. Please skip to section 4.3.8 on page 68 if you use Matlab to generate the graphics les (although you may want to take a brief look at the examples on the following pages to learn about exibility or legends). Lets start with two examples. Suppose you generate a surface plot with Matlab and want to include it in pgfplots. We have the matlab script[x,y]=meshgrid(linspace(0,1,120)); surf(x,y,sin(8*pi*x).* exp(-20*(y-0.5).^2) + exp(-(x-0.5).^2*30 - (y-0.25).^2 - (x-0.5).*(y-0.25))) xlabel(x), ylabel(y) axis off print -dpng plotgraphics3dsurf

which generates the gure in question. After automatically computing a tight bounding box for plotgraphics3dsurf.png (I used gimps Image Autocrop feature), and making the background color transparent (gimp: select the outer white space with the magic wand, then use12 Layer Transparency Color to Transparency) we get:

The key idea is now to identify several points in the image, and assign both their logical threedimensional coordinates and the corresponding twodimensional canvas coordinates in image coordinates. How? Well, the threedimensional coordinates are known to Matlab, it can display them for you if you click somewhere into the image, compare Figure 4.1 (left). The twodimensional canvas coordinates need work; they need to be provided relative to the lower left corner of the image. I used gimp and activated Points as units (lower left corner). The lower left corner now displays the image coordinates in pt which is compatible with pgfplots. An alternative to pointing onto coordinates is a measurement tool; compare Figure 4.1 (right) for the Measure tool in gimp which allows to compute the length of a line (in our case, the length of the lower left corner to the point of interest).12 I

have a german version, I am not sure if the translation is correct.

4.3. THE \ADDPLOT COMMAND: COORDINATE INPUT

65

I selected four points in the graphics and noted their 2d image coordinates and their 3d logical coordinates as follows:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the points key gets our collected coordinates as argument. It accepts a sequence of maps of the form 3d logical coordinate => 2d canvas coordinate . In our case, (0,1,0) has been found in the .png le at (0,207-112). Note that I introduced the dierence since gimp counts from the upper left, but pgfplots counts from the lower left. Once these four point coordinates are gathered, we nd Matlabs surface plot in a pgfplots axis. You can modify any appearance options, including dierent axis limits or further \addplot commands:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

pgfplots uses the four input points to compute appropriate x, y and z unit vectors (and the origin in graphics coordinates). These four vectors (with two components each) can be computed as a result of a linear system of size 8 8, that is why you need to provide four input points (each has two coordinates). pgfplots computes the unit vectors of the imported graphics, and afterwards it rescales the result such that it ts into the specied width and height. This rescaling respects the unit vector ratio (more precisely, it uses scale mode=scale uniformly instead of scale mode=stretch to fill). Consequently, the freedom to change the view of a threedimensional axis which contains a projected graphics is considerably smaller than before. Surprisingly, you can still change axis limits and width and height pgfplots will take care of a correct display of your imported graphics. Since version 1.6, you can also change zmin and/or zmax pgfplots will respect your changes as good as it can. Here is a further example. Suppose we are given the threedimensional visualization

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It has been generated by matlab (I only added transparency to the background with gimp). Besides advanced visualization techniques, it uses axis equal, i.e. unit vector ratio=1 1 1. As before, we need to identify four points, each with its 3d logical coordinates (from matlab) and the associated 2d canvas coordinates relative to the lower left corner of the graphics (note that there is a lot of white space around the graphics). Here is the output of pgfplots when you import the resulting graphics:Geometry provided by Sven Gro, Bonn http://www.igpm.rwth- aachen.de/DROPS % Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that I provided ve threedimensional coordinates here, but the last entry has no => mapping to two dimensional canvas coordinates. Thus, it is only used to update the bounding box (see the reference manual for the points key for details). The example above leads to a relatively small image and much empty space. This is due to the scale mode=scale uniformly implementation of pgfplots: it decided that the best way is to enlarge the involved axis limits. Here, best way means to satisfy width/height constraints combined with minimally enlarged (never shrinked) axis limits. The remaining degrees of freedom are width, height, and the axis limits. In our case, changing the ratio between width and height improves the display:

What happens is that pgfplots selects a single scaling factor which is applied to all units as they have been deduced from the points key. This ensures that the imported graphics ts correctly into the axis. In addition, pgfplots does its best to satisfy the remaining constraints. The complete description of how pgfplots scales the axis can be found in the documentation for scale mode=scale uniformly. Here is just a brief summary: pgfplots assumes that the prescribed width and height have to be satised. To this end, it rescales the projected unit vectors (i.e. the space which is taken up for each unit in x, y , and z ) and it can modify the axis limits. In the default conguration scale uniformly strategy=auto, pgfplots will never shrink axis limits. Compatibility remark: Note that the scaling capabilities have been improved for pgfplots version 1.6. In previous versions, only scale uniformly strategy=change vertical limits was available which lead to clipped axes. In short: please consider writing \pgfplotsset{compat=1.6} or newer into your document to benet from the improved scaling. If you have \pgfplotsset{compat=1.5} or older, the outcome for \addplot3 graphics will be dierent. We consider a third example which has been generated by the Matlab codeclear all close all seed = sum(clock) rand(seed,seed); X = rand(10,10,10); data = smooth3(X,box,5); p1 = patch(isosurface(data,.5), ... FaceColor,blue,EdgeColor,none); p2 = patch(isocaps(data,.5), ... FaceColor,interp,EdgeColor,none); isonormals(data,p1) daspect([1 2 2]) view(3); axis vis3d tight camlight; lighting phong % print -dpng plotgraphics3withaxis axis off print -dpng plotgraphics3 save plotgraphics3.seed seed -ASCII % to reproduce the result

I only added background transparency with gimp and got the following graphics:

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We proceed as before and collect four points, each with 3d logical coordinates (by clicking into the matlab gure) and their associated 2d canvas (graphics) coordinates using the measure tool of gimp. The result is shown in the code example below.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that it has non-standard data aspect ratio which is respected by pgfplots automatically.

External Three-Dimensional Graphics and Matlab

An extension by J urnjakob Dugge The procedure to map threedimensional logical coordinates to twodimensional canvas coordinates is tedious. J urnjakob Dugge contributed a script which does most of the logic and your work is reduced to a copy paste job. With his permission, I post the contribution here. The idea is to start a simple script which records mappings for any coordinates which have been clicked by the user. It works as follows: 1. Create the Matlab plot, say, usinghist3(randn(10000,2)) % some random data set(get(gca,child),FaceColor,interp,CDataMode,auto); % colors % make sure the "print" paper format is the same as the screen paper format: set(gcf,PaperPositionMode,auto)

% The function that gets called on each Data Cursor click function [txt] = myupdatefcn(obj,event_obj) % Get the screen resolution, in dots per inch dpi = get(0,ScreenPixelsPerInch); % Get the click position in pixels, relative to the lower left of the % screen screen_location=get(0,PointerLocation); % Get the position of the plot window, relative to the lower left of % the screen figurePos = get(gcf,Position); % Get the data coordinates of the cursor pos = get(event_obj,Position); % Format the data and figure coordinates. The factor "72.27/dpi" is % necessary to convert from pixels to TeX points (72.27 poins per inch) display([(,num2str(pos(1)),,,num2str(pos(2)),,,num2str(pos(3)),) => (, ... num2str((screen_location(1)-figurePos(1))*72.27/dpi),,, ... num2str((screen_location(2)-figurePos(2))*72.27/dpi),)]) % Format the tooltip display txt = {[X: ,num2str(pos(1))],[Y: ,num2str(pos(2))],[Z: ,num2str(pos(3))]};

Run pgfplotscsconversion, click on four points in your plot. Preferably select non-colinear points near the edges of the plot. Copy and paste the four lines that were written to the Matlab command window. Make sure that the rst two points have dierent X and Y values on screen (i.e. image canvas coordinates). 3. Export the plot as an imageaxis off print -dpng matlabout -r400 % PNG called "matlabout.png" with 400 dpi resolution

If you want to export vectors graphics, you should note that pdf output of Matlab is clumsy. It might be best to export to eps rst, followed by a conversion from eps to pdf. If you really want to use pdf output of Matlab, you may need to set the paper size to match the gure size by yourself, since the PDF driver does not automatically adjust the size:% It might be better to use print -depsc followed by epstopdf. % Use this if you (really) want to use print -dpdf: currentScreenUnits=get(gcf,Units) % Get current screen units currentPaperUnits=get(gcf,PaperUnits) % Get current paper units set(gcf,Units,currentPaperUnits) % Set screen units to paper units plotPosition=get(gcf,Position) % Get the figure position and size set(gcf,PaperSize,plotPosition(3:4)) % Set the paper size to the figure size set(gcf,Units,currentScreenUnits) % Restore the screen units print -dpdf matlabout % PDF called "matlabout.pdf"

4. Include the image in your pgfplots axis. If you selected points on the plot corners, your xmin, xmax, ymin and ymax should be set automatically, otherwise you may want to provide those yourself. Also, adjustments of width and height might be of interest to get the right vertical placement of the plot. Consider changing zmin and/or zmax to t your needs (preferrably only one of them; otherwise pgfplots may be unable to x the height).

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This contribution is from http://tex.stackexchange.com/questions/52987/3-dimensional-histogram-in-pgfplots .

Summary: External Three-Dimensional Graphics

As has been shown in the previous sections, \addplot3 graphics allows to include three-dimensional graphics and pgfplots overlays a exible axis with all its power. The cost to do so is 1. collect both logical threedimensional coordinates and imageinternal twodimensional coordinates for four points of your graphics. In Matlab, this can be simplied by the tool mentioned on page 68. 2. If your axes form a righthandedcoordinate system, that is all. If not, also add x dir=reverse for any reversed axes. Consider the following list of you encounter problems while working with \addplot3 graphics: It must be possible to deduce the origin and the three (twodimensional) unit vectors from the four provide points; otherwise the algorithm will fail.

The algorithm should detect any deciancies. However, if you encounter strange Dimension too large messages here, you can try other arguments in points. Take a look into your log le, it will probably indicate the source of problems (or use the debug key). Ensure that the external graphics has an orthogonal axis. In fact, the axis may be skewed (just like a pgfplots axis can be created by means of custom x, y, and z vectors). However, the external image must not have perspective projection as this is unsupported by pgfplots. The points command needs to receive four points which belong to linearly independent position vectors. pgfplots uses the rst two points to squeeze the graphics into the desired coordinates (which implies that they should not have the same canvas X or Y coordinates). It veries that the remaining points arguments are projected correctly. The resulting scaling by means of scale mode=scale uniformly will try to satisfy all scaling constraints. You can change these constraints by modifying width, height, xmin, xmax, ymin, ymax, zmin, zmax and/or any combination of these parameters. See also unit rescale keep size which controls the exibility of limit changes. There is also a key scale uniformly strategy which allows to select a dierent scaling strategy. The image should have a righthandedcoordinate system: you should be able to take your right hand, point your thumb in direction of the x axis, your rst nger in direction of y , and your second nger in direction of the z axis. If that is impossible, once of your axes is reversed and you need to communicate that to pgfplots explicitly by means of the x dir=reverse key (and its variants). Note that this feature has been veried with standard cartesian axes only. There is a debug key to investigate what the algorithm is doing:

/pgfplots/plot graphics/debug=true|false|visual

(initially false)

If you provide \addplot3 graphics[debug,points={...}], pgfplots will provide debug information onto your terminal and into the logle. It will also generate extra les containing the determined unit vectors and the linear system used to derive them (one such le for every \addplot3 graphics statement, the lename will be the graphics le name and .dat appended). Without the debug key, only the log le will contain brief information what pgfplots is doing behind the scenes. The choice true activates log messages. The choice visual activates log messages and places some lled circles at the provided points. The choice false disables all debug features.

4.3.9

Reading Coordinates From Files

4.4. ABOUT OPTIONS: PRELIMINARIES

71

Deprecation note: If you have data les, you should generally use \addplot table. The input type \addplot file is almost the same, but considerably less powerful. It is only kept for backwards compatibility. The \addplot file input mechanism is similar to the Tik Z-command plot file. It is to be used like\addplot file {datafile.dat};

where name is a text le with at least two columns which will be used as x and y coordinates. Lines starting with % or # are ignored. Such les are often generated by gnuplot:#Curve 0, 20 points #x y type 0.00000 0.00000 i 0.52632 0.50235 i 1.05263 0.86873 i 1.57895 0.99997 i ... 9.47368 -0.04889 i 10.00000 -0.54402 i

which allows to skip over a non-comment header line. This allows to read the same input les as plot table by skipping over column names. Please note that comment lines do not count as lines here. The input method plot file can also read meta data for every coordinate. As already explained for plot coordinates (see above), meta data can be used to change colors or other style parameters for every marker separately. Now, if point meta is set to explicit or to explicit symbolic and the input method is plot file, one further element will be read from disk for every line. Meta data is always the last element which is read. See page 98 for information and examples about per point meta data and page 100 for an application example using scatter/classes. Plot le is very similar to plot table: you can achieve the same eect with\addplot table[x index=0,y index=1,header=false] {datafile.dat};

Due to its simplicity, plot file is slightly faster while plot table allows higher exibility. Technical note: every opened le will be protocolled into your log le. The le can contain empty lines to tell pgfplots that the function has jumps. To use it, simply insert an empty line (and ensure that you have \pgfplotsset{compat=1.4} or newer in your preamble). See the documentation of empty line for details. /pgfplots/plot file/skip first=true|false /pgfplots/plot file/ignore first=true|false (initially false) (initially false)

The two keys can be provided as arguments to \addplot file[ options ] { lename }; to skip the rst non-comment entry in the le. They are equivalent. If you provide them in this context, the prex /pgfplots/plot file can be omitted.

4.4

About Options: Preliminaries

pgfplots knows a whole lot of keyvalue options which can be (re)dened to activate desired features or modied to apply some ne-tuning. A key usually has a value (like a number, a string, or perhaps some macro code). You can assign values A to keys (set keys) in many places in a L TEX document. The value will remain eective until it is changed or until the current TEX scope ends (which happens after a closing curly brace }, after \end{ name } or, for example, after \addplot). Most keys can be used like

CHAPTER 4. THE REFERENCE

axis-wide keys

which changes them for the complete axis. A key in this context can be any option dened in this manual, no matter if it has the /pgfplots/ or the /tikz/ key prex. Note that key prexes can be omitted in almost all cases. A value can usually be provided without curly braces. For example, if the manual contains something like xmin={ x coordinate }, you can safely skip the curly braces. The curly braces are mandatory if values contain something which would otherwise confuse the key setup (for example an equal sign = or a comma ,). Some keys can be changed individually for each plot:\begin{tikzpicture} \begin{axis} % keys valid for single plots: \addplot ...; % \addplot[key=value,key2=value2] ... ; % \addplot+[key=value,key2=value2] ... ; % \end{axis} \end{tikzpicture}

Besides these two possibilities, it is also possible to work with document-wide keys:\chapter{My Section} \pgfplotsset{ key=value, key2=value2, } This section has a common key configuration: \begin{tikzpicture} \begin{axis}% uses the key config from above ... \end{axis} \end{tikzpicture}

In the example above, the \pgfplotsset command changes keys. The changes are permanent and will be used until you redene them or the current environment (like \end{figure}) is ended or TEX encounters a closing brace }.

This includes documentwide preamble congurations like

The basic engine to manage keyvalue pairs is pgfkeys which is part of pgf. This engine always has a key name and a key path, which is somehow similar to le name and directory of les. The common directory (key path) of pgfplots is /pgfplots/. Although the key denitions below provide this full path, it is always (well, almost always) safe to skip this prex pgfplots uses it automatically. The same holds for the prexes /tikz/ which are common for all Tik Z drawing options and /pgf/ which are for the (more or less) lowlevel commands of pgf. All these prexes can be omitted. One important concept is the concept of styles. A style is a key which contains one or more other keys. It can be redened or modied until it is actually used by the internal routines. Each single component of Tik Z and pgfplots can be congured with styles. For example,

4.4. ABOUT OPTIONS: PRELIMINARIES

\pgfplotsset{legend style={line width=1pt}}

73

sets the line width for every legend to 1pt by appending line width=1pt to the existing style for legends. There are keys like legend style, ticklabel style, and label style which allow to modify the predened styles (in this case the styles for legends, ticklabels and axis labels, respectively). They are, in general, equivalent to a style name /.append style={} command (the only dierence is that the /.append style thing is a little bit longer). There is also the possibility to dene a new style (or to overwrite an already existing one) using /.style={}. There are several other styles predened to modify the appearance, see Section 4.18. \pgfplotsset{ key-value-list } Denes or sets all options in key-value-list . The key-value-list can contain any of the options in this manual which have the prex /pgfplots/ (however, you do not need to type that prex). Inside of key-value-list , the prexes /pgfplots/ which are commonly presented in this manual can be omitted (they are checked automatically). This command can be used to dene default options for the complete document or a part of the document. For example,\pgfplotsset{ cycle list={% {red, mark=*}, {blue,mark=*}, {red, mark=x}, {blue,mark=x}, {red, mark=square*}, {blue,mark=square*}, {red, mark=triangle*}, {blue,mark=triangle*}, {red, mark=diamond*}, {blue,mark=diamond*}, {red, mark=pentagon*}, {blue,mark=pentagon*} }, legend style={ at={(0.5,-0.2)}, anchor=north, legend columns=2, cells={anchor=west}, font=\footnotesize, rounded corners=2pt, }, xlabel=$x$,ylabel=$f(x)$ }

can be used to set document-wise styles for line specications, the legends style and axis labels. The settings remain in eect until the end of the current environment (like \end{figure}) or until you redene them or until the next closing curly brace } (whatever comes rst). You can also dene new styles (collections of keyvaluepairs) with /.style and /.append style.\pgfplotsset{ My Style 1/.style={xlabel=$x$, legend entries={1,2,3} }, My Style 2/.style={xlabel=$X$, legend entries={4,5,6} } }

The /.style and /.append style key handlers are described in Section 4.18 in more detail. Key handler key /.code={ TEX code } Occasionally, the pgfplots user interface oers to replace parts of its routines. This is accomplished using so called code keys. What it means is to replace the original key and its behavior with new TEX code . Inside of TEX code , any command can be used. Furthermore, the #1 pattern will be the argument provided to the key. Ive been invoked with this here\pgfplotsset{ My Code/.code={Ive been invoked with #1}} \pgfplotsset{My Code={this here}}

The example denes a (new) key named My Code. Essentially, it is nothing else but a \newcommand, plugged into the key-value interface. The second statement invokes the code key. Key handler key /.code 2 args={ TEX code } As /.code, but this handler denes a key which accepts two arguments. When the so dened key is used, the two arguments are available as #1 and #2.

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Key handler key /.cd Each key has a fully qualied name with a (long) prex, like /pgfplots/xmin. However, if the current directory is /pgfplots, it suces to write just xmin. The /.cd key handler changes the current directory in this way. The prexes /tikz/ and /pgfplots/ are checked automatically for any argument provided to \begin{axis}[ options ] or \addplot. So, you wont need to worry about them, just omit them and look closer in case the package doesnt identify the option.

4.4.1

Pgfplots and Tik Z Options

This section is more or less technical and can be skipped unless one really wants to know more about this topic. Tik Z options and pgfplots options can be mixed inside of the axis arguments and in any of the associated styles. For example,\pgfplotsset{every axis legend/.append style={ legend columns=3,font=\Large}}

assigns the legend columns option (a pgfplots option) and uses font for drawing the legend (a Tik Z option). The point is: legend columns needs to be known before the legend is typeset whereas font needs to be active when the legend is typeset. pgfplots sorts out any key dependencies automatically: The axis environments will process any known pgfplots options, and all everystyles will be parsed for pgfplots options. Every unknown option is assumed to be a Tik Z option and will be forwarded to the associated Tik Z drawing commands. For example, the font=\Large above will be used as argument to the legend matrix, and the font=\Large argument in\pgfplotsset{every axis label/.append style={ ylabel=Error,xlabel=Dof,font=\Large}}

will be used in the nodes for axis labels (but not the axis title, for example). It is an error if you assign incompatible options to axis labels, for example xmin and xmax cant be set inside of every axis label.

4.5

Two Dimensional Plot Types

pgfplots supports several two-dimensional line plots like piecewise linear line plots, piecewise constant plots, smoothed plots, bar plots and comb plots. Most of them use the pgf plot handler library directly, see [5, section 18.8]. Plot types are part of the plot style, so they are set with options. Most of the basic 2d plot types are part of Tik Z, see [5, section 18.8], and are probably known to users of Tik Z. They are documented here as well.

Constant plots draw lines parallel to the x-axis to connect coordinates. The discontinuous edges may be drawn or not, and marks may be placed on left or right ends. /tikz/const plot \addplot+[const plot] Connects all points with horizontal and vertical lines. Marks are placed left-handed on horizontal line segments, causing the plot to be right-sided continuous at all data points.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.5. TWO DIMENSIONAL PLOT TYPES

77

Note that symmetric is only true for constant mesh width: if the xdistances between adjacent data points dier, const plot mark mid will produce vertical lines in the middle between each pair of consecutive points. /tikz/jump mark left \addplot+[jump mark left] A variant of const plot mark left which does not draw vertical lines. 100% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Bar plots place horizontal or vertical bars at coordinates. Multiple bar plots in one axis can be stacked on top of each other or aligned next to each other. /tikz/xbar \addplot+[xbar] Places horizontal bars between the (y = 0) line and each coordinate. This option is used on a per-plot basis and congures only the visualization of coordinates. The gurewide style /pgfplots/xbar also sets reasonable options for ticks, legends and multiple plots. (no value)

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Bars are centered at plot coordinates with width bar width. Using bar plots usually means more than just a dierent way of how to connect coordinates, for example to draw ticks outside of the axis, change the legends appearance or introduce shifts if multiple \addplot commands appear. There is a precongured style for xbar which is installed automatically if you provide xbar as argument to the axis environment which provides this functionality.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here xbar yields /pgfplots/xbar because it is an argument to the axis, not to a single plot. For bar plots, it is quite common to provide textual coordinates or even descriptive nodes near the bars. This can be implemented using the keys symbolic y coords and nodes near coords, respectively: yes no 0 1 2 3 3 4 #participants 5 6 7 7

The symbolic y coords denes a dictionary of accepted coordinates which are then expected in y coordinates and the nodes near coords key displays values as extra nodes (see their reference docu-

4.5. TWO DIMENSIONAL PLOT TYPES

79

mentations for details). The example employs enlarge y limits in order to get some more free space since the default spacing is not always appropriate for bar plots. Note that it might be quite important to include xmin=0 explicitly as in the example above. Without it, the lower bound will be used: Uses lowest x coords for xmin yes no 1 1 2 3 4 5 6 #participants 7 8 9 9

This style sets /tikz/xbar and some commonly used options concerning horizontal bars for the complete axis. This is automatically done if you provide xbar as argument to an axis argument, see above. The xbar style denes shifts if multiple plots are placed into one axis. It draws bars adjacent to each other, separated by shift for multiple plots . Furthermore, it sets the style bar cycle list and sets tick and legend appearance options. The style is dened as follows.\pgfplotsset{ /pgfplots/xbar/.style={ /tikz/xbar, bar cycle list, tick align=outside, xbar legend, /pgf/bar shift={% % total width = n*w + (n-1)*skip % i.e. subtract half for centering -0.5*(\numplotsofactualtype*\pgfplotbarwidth + (\numplotsofactualtype-1)*#1) % the 0.5*w is for centering (.5+\plotnumofactualtype)*\pgfplotbarwidth + \plotnumofactualtype*#1% }, }, }

The formula for bar shift assigns shifts dependent on the total number of plots and the current plots number. It is designed to ll a total width of nbar width+(n 1) shift for multiple plots . The 0.5 compensates for centering. /tikz/ybar \addplot+[ybar] Like xbar, this option generates bar plots. It draws vertical bars between the (x = 0) line and each input coordinate. (no value)

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The example above simply changes how input coordinates shall be visualized. As mentioned for xbar, one usually needs modied legends and shifts for multiple bars in the same axis. There is a predened style which installs these customizations when provided to the axis environment: 107 6 Population Houses 4 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1930 1940 1950 1960 1970 Far Near Here Annot

Here, ybar yields /pgfplots/ybar because it is an argument to the axis, not to a single plot. The style aects the rst three \addplot commands. Note that it shifts them horizontally around the plot coordinates. The fourth \addplot command is some kind of annotation which doesnt update limits. The ybar style can be combined with symbolic x coords in a similar way as described for xbar:

As for xbar, the bar width and shift can be congured with bar width and bar shift. However, the bar shift is better provided as argument to /pgfplots/ybar since this style will overwrite the bar shift. Thus, prefer /pgfplots/ybar=4pt to set the bar shift. Sometimes it is useful to write the y values directly near the bars. This can be realized using the nodes near coords method: 107% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/ybar={ shift for multiple plots }

(style, default 2pt)

As /pgfplots/xbar, this style sets the /tikz/ybar option to draw vertical bars, but it also provides commonly used options for vertical bars. If you supply ybar to an axis environment, /pgfplots/ybar will be chosen instead of /tikz/ybar. It changes the legend, draws ticks outside of the axis lines and draws multiple \addplot arguments adjacent to each other; blockcentered at the x coordinate and separated by shift for multiple plots . It will also install the bar shift for every node near coord. Furthermore, it installs the style bar cycle list. It is dened similarly to /pgfplots/xbar. /pgfplots/bar cycle list A style which installs cycle lists for multiple bar plots.\pgfplotsset{ /pgfplots/bar cycle list/.style={/pgfplots/cycle list={% {blue,fill=blue!30!white,mark=none},% {red,fill=red!30!white,mark=none},% {brown!60!black,fill=brown!30!white,mark=none},% {black,fill=gray,mark=none},% } }, }

(no value)

/pgf/bar width={ dimension or unit }

(initially 10pt)

Congures the width used by xbar and ybar. It is accepted to provide mathematical expressions. As of pgfplots 1.7, it is allows to provide an unit as bar width. In this case, the bar width will be interpreted as axis unit:

In order to interprete arguments as units, you have to write \pgfplotsset{compat=1.7} (or newer) into your preamble. Older versions will implicitly append the pt sux if the argument is no dimension. \pgfplotbarwidth A mathematical expression which results in the fully computed value of bar width (i.e. it includes any unit computations). Note that you may need to enlargelimits in order to see the complete bar pgfplots will not automatically update the axis limits to respect bar width. /pgf/bar shift={ dimension or unit } (initially 0pt)

Congures a shift for xbar and ybar. Use bar shift together with bar width to draw multiple bar plots into the same axis. It is accepted to provide mathematical expressions. As of pgfplots 1.7, it is allows to provide an unit as bar shift. In this case, the bar shift will be interpreted as axis unit. \pgfplotbarshift A mathematical expression which results in the fully computed value of bar shift (i.e. it includes any unit computations). Note that you may need to enlargelimits in order to see the complete bar pgfplots will not automatically update the axis limits to respect bar shift. /pgfplots/bar direction=auto|x|y (initially auto)

If pgfplots encounters a value bar width=1 (i.e. without dimension like 1pt), it attempts to evaluate the bars direction. The default conguration auto assumes that you write something like ybar,bar width=1. In this case, it is clear that you have a y bar and pgfplots assumes bar direction=y. However, this context information is unavailable. In this case, you can use the choice x if pgfplots in unaware that it works on an xbar plot or y if pgfplots is unaware that you meant an ybar plot.

84 /tikz/ybar interval \addplot+[ybar interval]

CHAPTER 4. THE REFERENCE (no value)

This plot type produces vertical bars with width (and shift) relatively to intervals of coordinates. There is one conceptional dierence when working with intervals: an interval is dened by two coordinates. Since ybar has one value for each interval, the ith bar is dened by 1. the y value of the ith coordinates, 2. the x value of the ith coordinate as left interval boundary, 3. the x value of the (i + 1)th coordinate as right interval boundary. Consequently, there is one coordinate too much : the last coordinate will only be used to determine the interval width; its y value doesnt inuence the bar appearance. It is installed on a per-plot basis and congures only the visualization of coordinates. See the style /pgfplots/ybar interval which congures the appearance of the complete gure. 4 3 2 1 0 0.2 0.4 0.6 0.8 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/ybar interval={ relative width } (style, default 1) A style which is intended to install options for ybar interval for a complete gure. This includes tick and legend appearance, management of multiple bar plots in one gure and a more adequate cycle list using the style bar cycle list. /tikz/xbar interval \addplot+[xbar interval] As ybar interval, just for horizontal bars.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.5. TWO DIMENSIONAL PLOT TYPES

87

The base point (x, y ) is provided as before; in the example above, it is generated by plot expression and yields (x, x2 ). The vector direction (u, v ) needs to be given in addition. Our example with quiver/u=1 and quiver/v=2*x results in u = 1 and v = 2x. Thus, we have dened and visualized a vector eld for the derivative of f (x) = x2 . A common example is to visualize the gradient (x f, y f )(x, y ) of a twodimensional function f (x, y ): x exp(x2 y 2 ) and its gradient% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example visualizes f (x, y ) = x exp(x2 y 2 ) using contour gnuplot as rst step. The options contour/number and contour/labels provide ne-tuning for the contour and are not of interest here (so is the axis background which just improves visibility of contour lines). What we are interested in is the quiver= style: it denes u and v to some twodimensional expressions. Furthermore, we used quiver/scale arrows to reduce the arrow size. The -stealth is a Tik Z style which congures outgoing arrow styles of type stealth. The samples=15 key congures how we get our input data. In our case, we have input data (xi , yj , f (xi , yj )) with 15 samples for each, i and j . It is also possible to place quiver plots on a prescribed z value:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the quiver plots is placed on top of a surf. It visualizes the gradient (using a common scale factor of 1/10 to reduce the arrow lengths). The quiver/w=0 means that arrows have no z dierence, and the {1} argument indicates that all start at (xi , yj , 1). Here, the values (xi , yj ) are sampled in the domain=0:1 argument (with samples=10), i.e. arrows start at (xi , yj , 1) and end at (xi + yj /10, yj + xi /10, 1). So far, quiver plots do not assume a special sequence of input points. This has two consequences: rst, you can plot any vector eld by considering just (x, y ) + (u, v ) (or (x, y, z ) + (u, v, w)) the data doesnt necessarily need to be a twodimensional function (as opposed to surf etc). On the other hand, you need to provide quiver/scale arrows manually since quiver doesnt know the mesh width in case you provide matrix data13 . Note that quiver plots are currently not available together with logarithmic axes.I might add something like quiver/scale arrows=auto in the future, I dont know yet. Loops through input data are slow in TEX, automatic mesh widths computation even more...13 Actually,

CHAPTER 4. THE REFERENCE (initially 0) (initially 0) (initially 0)

These keys dene how the vector directions (u, v ) (or, for three dimensional plots, (u, v, w)) shall be set. The expression can be a constant expression like quiver/u=1 or quiver/u=42*5. It may also depend on the nal base point values using the values x, y or z as in the example above. In this context, x yields the x coordinate of the point where the vector starts, y the y coordinate and so on. Attention: the fact that x refers to the nal x coordinate means that parametric plots should use t as variable 14 . Consider the following example:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, a parametric plot is used to draw a circle and tangent vectors. The choice variable=\t plays a functional role besides naming conventions: it allows to access the parametric variable within the expressions for both u and v. On the other hand, we could have used u=y and v=-x since x expands to the x coordinate with value sin(deg(t)) and y expands to the y coordinate cos(deg(t)). Another important application is to use table column references like quiver/u=\thisrow{col} in conjunction with \addplot table: Quiver and plot table% Preamble: \pgfplotsset{width=7cm,compat=1.9}

These keys have the same function as quiver/u and its variants. However, they dont call the math parser, so only single values are allowed (including something like \thisrow{columnname}). /pgfplots/quiver/colored /pgfplots/quiver/colored={ color } (no value)

Allows to dene an individual color for each arrow. Omitting the argument color is identical to quiver/colored=mapped color which uses the point meta to get colors for every arrow. If you just want to set the same color for every arrow, prefer using \addplot[blue,quiver] which is more ecient. /pgfplots/quiver/scale arrows={ scale } (initially 1)

Allows to rescale the arrows by a factor. This may be necessary if the arrow length is longer than the distance between adjacent base points (xi , yi ). There may come a feature to rescale them automatically. /pgfplots/quiver/update limits=true|false /pgfplots/quiver/every arrow Allows to provide individual arrow styles. The style can contain any Tik Z drawing option. It will be evaluated for every individual arrow and may depend upon anything which is available at visualization time. In particular, this includes point meta data, typically using \pgfplotspointmetatransformed [0, 1000] where 0 corresponds to point meta min and 1000 corresponds to point meta max: Thickness indicates strength.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

In the example, we have some 2d vector eld stored in helper constants \U and \V. The length of each vector is stored in \LEN here. The quiver plot as such contains unit length vectors and the \LEN enters an every arrow style to get varying line width. An every arrow style might also depend upon mapped color (provided point meta has been set). Again, if you do not need individual arrow styles, prefer using a plot style (cycle list or argument to \addplot) which is more ecient. /pgfplots/quiver/before arrow/.code={ ... }

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Advanced keys for more ne tuning of the display. They allow to install some TEX code manually before or after the drawing operations for single arrows. Both are initially empty. /pgfplots/quiver/quiver legend It is implicitly activated whenever quiver plot handlers are selected.100 0 100 6 4 2 0 2 4 6 Legend % Preamble: \pgfplotsset{width=7cm,compat=1.9}

(style, no value)

A style which redenes legend image code in order to produce a suitable legend for quiver plots.

Allows stacking of plots in either x or y direction. Stacking means to add either x- or y coordinates of successive \addplot commands on top of each other. 6% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The current implementation for stack plots does not interpolate missing coordinates. That means stacking will fail if the plots have dierent grids. /pgfplots/ybar stacked=plus|minus (style, default plus)

The plot handler stack plots is particularly useful for bar plots. There are two possible modes of operation: the rst is to set stack plots=y,/tikz/ybar. It activates just these two features without making them aware of each other. The second is to set ybar stacked which activates the two features and makes them aware of each other. If you use stack plots together with /tikz/ybar, you have kind of a lowlevel implementation which is kind of raw:

Using ybar stacked enables stacked vertical bars (i.e. ybar and stack plots=y) and it also adjusts the legend and tick appearance and assigns a useful cycle list. To this end, it should be given as option to the axis:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(style, default plus)

The same remarks as for ybar stacked hold for xbar stacked as well: xbar stacked is a gure-wide style which enables stacked horizontal bars (i.e. xbar and stack plots=x). It also adjusts the legend and tick appearance and assigns a useful cycle list. Consequently, one can have a raw picture which combines stacking and bars as in the following picture (i.e. without xbar stacked):

/pgfplots/reverse stacked plots=true|false

Congures the sequence in which stacked plots are drawn. This is more or less a technical detail which should not be changed in any normal case.

The motivation is as follows: suppose multiple \addplot commands are stacked on top of each other and they are processed in the order of appearance. Then, the second plot could easily draw its lines (or ll area) on top of the rst one - hiding its marker or line completely. Therefor, pgfplots reverses the sequence of drawing commands. This has the side-eect that any normal Tik Z-paths inside of an axis will also be processed in reverse sequence. /pgfplots/stacked ignores zero=true|false (initially true, default true)

/pgfplots/ybar interval stacked=plus|minus

It is possible to combine ybar stacked and xbar stacked with nodes near coords. In contrast to nonstacked plots, it appears to be of limited use to draw a node near the top of the stack. Instead, one typically wants to see the dierence added in each stacking step. To this end, pgfplots will automatically recongure nodes near coords to display the added values in the center of each new bar:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that the preceding example contains no nodes for coordinates with value 0. This is due to the key stacked ignores zero which is active if compat=1.9 or newer: empty increments will be discarded. This automatic reconguration is essentially part of the styles xbar stacked or ybar stacked: both recongure nodes neard coords. Note that this feature has been introduced in version 1.9. In order to maintain backwards compatible to previous work-arounds, you have to write compat=1.9 to get these eects.

Area plots may need modied legends, for example using the area legend key. Furthermore, one may want to consider the axis on top key such that lled areas do not overlap ticks and grid lines. /pgfplots/area style A style which sets\pgfplotsset{ /pgfplots/area style/.style={% area cycle list, area legend, axis on top, }}

(style, no value)

/pgfplots/area cycle list

(style, no value)

A style which installs a cycle list suitable for area plots. The initial conguration of this style simply invokes the bar cycle list which does also provide lled plot styles.

The most simple scatter plots produce the same as the line plots above but they contain only markers. They are enabled using the only marks key of Tik Z. /tikz/only marks \addplot+[only marks] Draws a simple scatter plot: all markers have the same appearance. 1 0.5 0 0.5 4 2 0 2 4% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The only marks visualization style simply draws marks at every coordinate. Marks can be set with mark= mark name and marker options like size and color can be specied using the mark options= style options key (or by modifying the every mark style). The available markers along with the accepted style options can be found in Section 4.7 on page 155. More sophisticated scatter plots change the marker appearance for each data point. An example is that marker colors depend on the magnitude of function values f (x) or other provided coordinates. The term scatter plot will be used for this type of plot in the following sections.

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Scatter plots require source coordinates. These source coordinates can be the y coordinate, or explicitly provided additional values. /pgfplots/scatter \addplot+[scatter] Enables marker appearance modications. The default implementation acquires source coordinates for every data point (see scatter src below) and maps them linearly into the current color map. The resulting color is used as draw and ll color of the marker.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Scatter plots can be congured using a set of options. One of them is mandatory, the rest allows ne grained control over marker appearance options. /pgfplots/scatter src=none| expression |x|y|z|f(x)|explicit|explicit symbolic (initially none)

This key is necessary for any scatter plot and it is set to f(x) as soon as scatter is activated and no dierent choice has been made. It needs to be provided as option for \addplot to congure the value used to determine marker appearances. Actually, scatter src is nothing but an alias for point meta, so the main documentation for this key is on page 180. However, we summarize the choices here together with scatter plot examples. Usually, scatter src provides input data (numeric or string type) which is used to determine colors and other style options for markers. The default conguration expects numerical data which is mapped linearly into the current color map. The value of scatter src determines how to get this data: the choices x, y and z will use either the x, y or z coordinates to determine marker options. Any coordinate lters, logarithms or stacked-plot computations have already been applied to these values (use rawx, rawy and rawz for unprocessed values). The special choice f(x) is the same as y for two dimensional plots and the same as z for three dimensional plots. The choice explicit expects the scatter source data as additional coordinate from the coordinate input streams (see Section 4.3.1 for how to provide input meta data or below for some

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small examples). They will be treated as numerical data. The choice explicit symbolic also expects scatter source data as additional meta information for each input coordinate, but it treats them as strings, not as numerical data. Consequently, no arithmetics is performed. It is the task of the scatter plot style to do something with it. See, for example, the scatter/classes style below. Finally, it is possible to provide an arbitrary mathematical expression which involves zero, one or more of the values x (the current x coordinate), y (the current y coordinate) or z (the current z coordinate, if any). If data is read from tables, mathematical expressions might also involve \thisrow{ column name } or \thisrowno{ column index } to access any of the table cells in the current row. Here are examples for how to provide data for the choices explicit and explicit symbolic.\begin{tikzpicture} \begin{axis} % provide color data explicitly using [<data>] % behind coordinates: \addplot+[scatter,scatter src=explicit] coordinates { (0,0) [1.0e10] (1,2) [1.1e10] (2,3) [1.2e10] (3,4) [1.3e10] % ... }; % Assumes a datafile.dat like % xcolname ycolname colordata % 0 0 0.001 % 1 2 0.3 % 2 2.1 0.4 % 3 3 0.5 % ... % the file may have more columns. \addplot+[scatter,scatter src=explicit] table[x=xcolname,y=ycolname,meta=colordata] {datafile.dat}; % Same data as last example: \addplot+[scatter,scatter src=\thisrow{colordata}+\thisrow{ycolname}] table[x=xcolname,y=ycolname] {datafile.dat}; % Assumes a datafile.dat like % 0 0 0.001 % 1 2 0.3 % 2 2.1 0.4 % 3 3 0.5 % ... % the first three columns will be used here: \addplot+[scatter,scatter src=explicit] file {datafile.dat}; \end{axis} \end{tikzpicture}

This style is installed by default. When active, it recomputes the color mapped color for every processed point coordinate by transforming the scatter src coordinates into the current color map linearly. Then, it evaluates the options provided as options for each marker which are expected to depend on mapped color. The user interface for color maps is described in Section 4.7.6.

This key is actually a style which redenes @pre marker code and @post marker code (see below). Remark: The style use mapped color re denes @pre marker code and @post marker code. There is a starred variant use mapped color* which appends the functionality while keeping the old marker code. /pgfplots/scatter/classes={ styles for each class name } A scatter plot style which visualizes points using several classes. The style assumes that every point coordinate has a class label attached, that means the choice scatter src=explicit symbolic is as-

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sumed15 . A class label can be a number, but it can also be a symbolic constant. Given class labels for every point, styles for each class name contains a comma-separated list which associates appearance options to each class label.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

In this example, the coordinate (0.1,0.15) has the associated label a while (0.45,0.27) has the label c (see Section 4.3 for details about specifying point meta data). Now, the argument to scatter/classes contains styles for every label for label a, square markers will be drawn in color blue. The generation of a legend works as for a normal plot but scatter/classes requires one legend entry for every provided class. It communicates the class labels to the legend automatically. It works as if there had been dierent \addplot commands, one for every class label. It is also possible to provide scatter/classes as argument to a single plot, allowing dierent scatter plots in one axis.15 If scatter src is not explicit symbolic, we expect a numeric argument which is rounded to the nearest integer. The resulting integer is used a class label. If that fails, the numeric argument is truncated to the nearest integer. If that fails as well, the point has no label.

In general, the format of styles for each class name is a comma separated list of label ={ style options }. Attention: The keys every mark and mark options have no eect when used inside of styles for each class name ! So, instead of assigning mark options, you can simply provide the options directly. They apply only to markers anyway. Remark: To use \label and \ref in conjunction with scatter/classes, you can provide the class labels as optional arguments to \label in square brackets:\addplot[ scatter/classes={ a={mark=square*,blue},% b={mark=triangle*,red},% c={mark=o,draw=black,fill=black}% }, scatter,only marks, scatter src=explicit symbolic] % [and coordinate input here... ] ; \label[a]{label:for:first:class} \label[b]{label:for:second:class} \label[c]{label:for:third:class} ... First class is \ref{label:for:first:class}, second is \ref{label:for:second:class}.

Remark: It is possible to click into the plot to display labels with mouse popups, see the clickable coords key of the clickable library.

0.2 0.1 0.2 0.4

0.2 0.1 0.6

The content is, if nothing else has been specied, the content of the point meta, displayed using the default content =\pgfmathprintnumber{\pgfplotspointmeta}. The macro \pgfplotspointmeta contains whatever has been selected by the point meta key, it defaults to the y coordinate for two dimensional plots and the z coordinate for three dimensional plots. Since point meta=explicit symbolic allows to treat string data, you can provide textual descriptions which will be shown inside of the generated nodes16 : (3)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The square brackets are the way to provide explicit point meta for plot coordinates. Please refer to the documentation of plot file and plot table for how to get point meta from les. The content can also depend on something dierent than \pgfplotspointmeta. But since content is evaluated during \end{axis}, pgfplots might not be aware of any special information inside of content youll need to communicate it to pgfplots with the visualization depends on key as follows:16 In

The example uses a scatter plot to get dierent colors, where the scatter src (or, equivalently, point meta) is already used to dene the markers color. In addition to the colored scatter plot, wed like to add nodes near coords, where the displayed nodes should contain \thisrow{myvalue}. To do so, we dene scatter,point meta=\thisrow{color} (just as described in the previous sections). Furthermore, we use nodes near coords* in order to combine dierent scatter styles (see below for details). The value for nodes near coords* depends on \thisrow{myvalue}, but we cant use \pgfplotspointmeta (which is already occupied). Thus, we communicate the additional input data by means of visualization depends on={\thisrow{myvalue} \as \myvalue}. The statement denes a new macro, \myvalue, and assigns the value \thisrow{myvalue}. Furthermore, it congures pgfplots to remember this particular macro and its contents until \end{axis} (see the documentation for visualization depends on for details). The style nodes near coords might be useful for bar plots, see ybar for an example of nodes near coords. Remarks and Details: nodes near coords uses the same options for line styles and colors as the current plot. This may be changed using the style every node near coord, see below. nodes near coords is actually one of the scatter plot styles. It redenes scatter/@pre marker code to generate several Tik Z \node commands. In order to use nodes near coords together with other scatter plot styles (like scatter/use mapped color or scatter/classes), you may append a star to each of these keys. The variant nodes near coords* will append code to scatter/@pre marker code without overwriting the previous value. Consider using enlargelimits together with nodes near coords if text is clipped away.

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Currently nodes near coords does not work satisfactorily for ybar interval or xbar interval, sorry.

/pgfplots/every node near coord A style used for every node generated by nodes near coords. It is initially empty. /pgfplots/nodes near coords align={ alignment method } Species how to align nodes generated by nodes near coords. Possible choices for alignment method are

(style, no value) (initially auto)

auto uses horizontal if the x coordinates are shown or vertical in all other cases. This checks the current value of point meta. horizontal uses left if \pgfplotspointmeta < 0 and right otherwise. vertical uses below if \pgfplotspointmeta < 0 and above otherwise. It is also possible to provide any Tik Z alignment option such as anchor=north east, below or something like that. It is also allowed to provide multiple options. /pgfplots/scatter/position=absolute|relative (initially relative) Allows to choose how to position scatter plot markers. This applies only if the scatter option is true. The choice relative is the initial conguration, it means that the scatter marker is placed at the given points coordinates. Technically, it means that the transformation matrix is shifted such that (0,0) is right at the current points coordinates. This is typically what you want. The choice absolute allows to position a scatter plot marker absolutely, for example by means of axis cs. This can be combined with nodes near coords and a suitable set of options in every node near coord/.style={ options }: one could say at={(axis cs:\coordindex,\coordindex*5)} or something like that. Note that this choice necessarily needs an at key to specify the nodes position, otherwise its position will be undened17 . /pgfplots/scatter/@pre marker code/.code={ ... } /pgfplots/scatter/@post marker code/.code={ ... } These two keys constitute the public interface which determines the marker appearance depending on scatter source coordinates. Redening them allows ne grained control even over marker types, line styles and colors. The scatter plot algorithm works as follows: 1. The scatter source coordinates form a data stream whose data limits are computed additionally to the axis limits. This step is skipped for symbolic meta data. 2. Before any markers are drawn, a linear coordinate transformation from these data limits to the interval [0.0, 1000.0] is initialised. 3. Every scatter source coordinate18 will be transformed linearly and the result is available as macro \pgfplotspointmetatransformed [0.0, 1000.0]. The decision is thus based on per thousands of the data range. The transformation is skipped for symbolic meta data (and the meta data is simply contained in the mentioned macro). 4. The pgf coordinate system is translated such that (0pt,0pt) is the plot coordinate. 5. The code of scatter/@pre marker code is evaluated (without arguments). 6. The standard code which draws markers is evaluated. 7. The code of scatter/@post marker code is evaluated (without arguments). The idea is to generate a set of appearance keys which depends on \pgfplotspointmetatransformed. Then, a call to \scope[ generated keys ] as @pre code and the associated \endscope as @post code will draw markers individually using [ generated keys ]. A technical example is shown below. It demonstrates how to write user dened routines, in this case a threeclass system19 .it will be the origin of the canvas. Which is not necessarily the same as the origin of your axis. the evaluation, the public macros \pgfplotspointmeta and \pgfplotspointmetarange indicate the source coordinate and the source coordinate range in the format a : b (for logaxis, they are given in xed-point representation and for linear axes in oating point). 19 Please note that you dont need to copy this particular example: the multipleclass example is also available as predened style scatter/classes.18 During 17 Well,

Please note that \ifdim compares TEX lengths, so the example employs the sux pt for any number used in this context. That doesnt change the semantics. The two (!) \expandafter constructions make sure that \scope is invoked with the content of \markopts instead of the macro name \markopts.

4.5.11

1D Colored Mesh Plots

(no value)

/pgfplots/mesh \addplot+[mesh]

Uses the current color map to determine colors for each xed line segment. Each line segment will get the same color.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The color data is per default the y value of the plot. It can be recongured using the point meta key (which is actually the same as scatter src). The following example provides the color data explicitly for plot coordinates, using the square bracket notation.

This one-dimensional mesh plot is actually a special case of the twodimensional mesh plots, so more detailed conguration, including how to change the color data, can be found in Section 4.6.5.

4.5.12

Interrupted Plots

Sometimes it is desirable to draw parts of a single plot separately, without connection between the parts (discontinuities). pgfplots oers two ways to generate interrupted plots: either using empty lines or by providing unbounded coords. The rst way is simple; it needs no extra key (only \pgfplotsset{compat=1.4} or newer in your preamble): Interrupted data plot 1,000% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(50,600) (60,800) (80,1000) }; \end{axis} \end{tikzpicture}

0 0 20 40 60 80

Here, pgfplots runs with the default conguration empty line=auto which interpretes empty lines as jump markers. This works for any data input method, i.e. using \addplot coordinates, \addplot table, and \addplot file. The second way to generate interrupted plots addresses the case where empty lines are unavailable or impossible (due to limitations of the tool generating the data le, for example). In this case, interrupted plots can be achieved using the unbounded coords key combined with coordinate values nan, inf or -inf. /pgfplots/unbounded coords=discard|jump (initially discard) This key congures what to do if one or more coordinates of a single point are unbounded. Here, unbounded means it is either (+inf or -inf) or it has the special notanumber value nan. The initial setting discard discards the complete point and a warning is issued in the log le20 . This setting has the same eect as if the unbounded point did not occur: pgfplots will interpolate between the bounded adjacent points.

The alternative jump allows interrupted plots: it provides extra checking for these coordinates and does not interpolate over them; only those line segments which are adjacent to unbounded coordinates will be skipped.20 The

For plot expression and its friends, it is more likely to get very large oating point numbers instead of inf. In this case, consider using the restrict x to domain key described on page 328. The unbounded coords=jump method does also work for mesh/surface plots: every face adjacent to an unbounded coordinate will be discarded in this case. The following example sets up a (cryptic) coordinate lter which cuts out a quarter of the domain and replaces its values with nan:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

More about this coordinate ltering can be found in Section 4.23 Skipping Or Changing Coordinates Filters.

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4.5.13

Patch Plots

Patch Plots visualize a sequence of one or more triangles (or other sorts of patches). These triangles can be drawn with a single color (shader=flat and shader=faceted interp) or with interpolated colors (shader=interp). There are both two- and three-dimensional patch plots, both with the same interface and the same keys. Therefore, the reference documentation for patch plots can be found in Section 4.6.12 together with threedimensional patch plots.

4.6

Three Dimensional Plot Types

pgfplots provides three dimensional visualizations like scatter, line, mesh or surface plots. This section explains the methods to provide input coordinates and how to use the dierent plot types.

4.6.1

Before You Start With 3D

Before we delve into the capabilities of pgfplots for three dimensional visualization, let me start with some preliminary remarks. The reason to use pgfplots for three dimensional plots are similar to those of normal, two dimensional plots: the possibility to get consistent fonts and document consistent styles combined with highquality output. While this works very nice for (not too complex) two dimensional plots, it requires considerably more eort than nongraphical documents. This is even more so for three dimensional plots. In other words: pgfplots three dimensional routines are slow. There are reasons for this and some of them may vanish in future versions. But one of these reasons is that TEX has never been designed for complex visualisation techniques. Consider the image externalization routines mentioned in Section 7.1, in particular the external library to reduce typesetting time. Besides the speed limitations, three dimensional plots reach memory limits easily. Therefore, the plot complexity of three dimensional plots is limited to relatively coarse resolutions. Section 7.1 also discusses methods to extend the initial TEX memory limits. Another issue which arises in three dimensional visualization is depth. pgfplots supports z buering techniques up to a certain extend. It works pretty well for single scatter plots (z buffer=sort), mesh or surface plots (z buffer=auto) or parametric mesh and surface plots (z buffer=sort). However, it cant combine dierent \addplot commands, those will be drawn in the order of appearance. You may encounter the limitations sometimes. Maybe it will be improved in future versions. If you decide that you need high complexity, speed and 100% reliable z buers (depth information), you should consider using other visualization tools and return to pgfplots in several years. If you can wait for a complex picture and you dont even see the limitations arising from z buering limitations, you should use pgfplots. Again, consider using the automatic picture externalization with the external library discussed in Section 7.1. Enough for now, lets continue.

4.6.2

\addplot3[ options ] input data

The \addplot3 Command: Three Dimensional Coordinate Input

trailing path commands ;

The \addplot3 command is the main interface for any three dimensional plot. It works in the same way as its two dimensional variant \addplot which has been described in all detail in Section 4.3 on page 42. The \addplot3 command accepts the same input methods as the \addplot variant, including expression plotting, coordinates, les and tables. However, a third coordinate is necessary for each of these methods which is usually straightforward and is explained in all detail in the following. Furthermore, \addplot3 has a way to decide whether a line visualization or a mesh visualization has to be done. The rst one is a map from one dimension into R3 and the latter one a map from two dimensions to R3 . Here, the keys mesh/rows and mesh/cols are used to dene mesh sizes (matrix sizes). Usually, you dont have to care about that because the coordinate input routines already allow either one- or two-dimensional structure. \addplot3 coordinates { coordinate list };

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\addplot3[ options ] coordinates { coordinate list } trailing path commands ; The \addplot3 coordinates method works like its twodimensional variant, \addplot coordinates which is described in all detail on page 45: A long list of coordinates ( x , y , z ) is expected, separated by white spaces. The input list can be either an unordered series of coordinates, for example for scatter or line plots. It can also have matrix structure, in which case an empty line (which is equivalent to \par) marks the end of one matrix row. Matrix structure can also be provided if one of mesh/rows or mesh/cols is provided explicitly.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, \addplot3 reads a matrix with three rows and four columns. The empty lines separate one row from the following. As for the twodimensional plot coordinates, it is possible to provide (constant) mathematical expressions inside of single coordinates. The syntax ( x , y , z ) [ meta ] can be used just as for two dimensional plot coordinates to provide explicit color data; error bars are also supported. \addplot3 file { name }; \addplot3[ options ] file { name } trailing path commands ; The \addplot3 file input method is the same as \addplot file it only expects one more coordinate. Thus, the input le contains xi in the rst column, yi in the second column and zi in the third. A further column is read after zi if point meta=explicit has been requested, see the documentation of \addplot file on page 70 for details. As for \addplot3 coordinates, an empty line in the le marks the end of one matrix row.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

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For matrix data in les, it is important to specify the ordering in which the matrix entries have been written. The default conguration is mesh/ordering=x varies, so you need to change it to mesh/ordering=y varies in case you have columnwise ordering. \addplot3 table [ column selection ]{ le }; \addplot3[ options ] table [ column selection ]{ le } trailing path commands ; The \addplot3 table input works in the same way as its two dimensional counterpart \addplot table. It only expects a column for the z coordinates. Furthermore, it interprets empty input lines as end ofrow (more generally, endofscanline) markers, just as for plot file. The remark above about the mesh/ordering applies here as well. /pgfplots/mesh/rows={ integer } /pgfplots/mesh/cols={ integer } For visualization of mesh or surface plots which need some sort of matrix input, the dimensions of the input matrix need to be known in order to visualize the plots correctly. The matrix structure may be known from endofrow marks (empty lines as general endofscanline markers in the input stream) as has been described above. If the matrix structure is not yet known, it is necessary to provide at least one of mesh/rows or mesh/cols where mesh/rows indicates the number of samples for y coordinates whereas mesh/cols is the number of samples used for x coordinates (see also mesh/ordering). Thus, the following example is also a valid method to dene an input matrix.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

It is enough to supply one of mesh/rows or mesh/cols the missing value will be determined automatically. If you provide one of mesh/rows or mesh/cols, any endofrow marker seen inside of input les or coordinate streams will be ignored. /pgfplots/mesh/scanline verbose=true|false (initially false)

A Provides debug messages in the L TEX output about endofscanline markers. The message will tell whether endofscanlines have been found and if they are the same.

/pgfplots/mesh/ordering=x varies|y varies|rowwise|colwise

(initially x varies)

Allows to congure the sequence in which matrices (meshes) are read from \addplot3 coordinates, \addplot3 file or \addplot3 table. Here, x varies means a sequence of points where n=mesh/cols successive points have the y coordinate xed. This is intuitive when you write down a function because x is horizontal and y vertical. Note that in matrix terminology, x refers to column indices whereas y refers to row indices. Thus, x varies is equivalent to rowwise ordering in this sense. This is the initial conguration.

(0,2,0) (1,2,0.7) (2,2,0.8) (3,2,0.5) }; \end{axis} \end{tikzpicture}

Note that mesh/ordering is mandatory, even though the size of the matrix can be provided in dierent ways. The example above uses empty lines to mark scanlines. One could also say mesh/rows=3 and omit the empty lines. Consequently, mesh/ordering=y varies provides points such that successive m=mesh/rows points form a column, i.e. the x coordinate is xed and the y coordinate changes. In this sense, y varies is equivalent to colwise ordering, it is actually a matrix transposition.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Again, note the subtle dierence to the common matrix indexing where a column has the second index xed. pgfplots refers to the way one would write down a function on a sheet of paper (this is consistent with how Matlab () displays discrete functions with matrices). \addplot3 { math expression } ; \addplot3[ options ] { math expression } trailing path commands ;

Expression plotting also works in the same way as for two dimensional plots. Now, however, a two dimensional mesh is sampled instead of a single line, which may depend on x and y. The method \addplot3 { math expr } visualizes the function f (x, y ) = math expr where f : [x1 , x2 ] [y1 , y2 ] R. The interval [x1 , x2 ] is determined using the domain key, for example using domain=0:1. The interval [y1 , y2 ] is determined using the y domain key. If y domain is empty, [y1 , y2 ] = [x1 , x2 ] will be assumed. If y domain=0:0 (or any other interval of length zero), it is assumed that the plot does not depend on y (thus, it is a line plot). The number of samples in x direction is set using the samples key. The number of samples in y direction is set using the samples y key. If samples y is not set, the same value as for x is used. If samples y 1, it is assumed that the plot does not depend on y (meaning it is a line plot).

A variant of \addplot3 expression which allows to provide dierent coordinate expressions for the x, y and z coordinates. This can be used to generate parametrized plots. Please note that \addplot3 (x,y,x^2) is equivalent to \addplot3 expression {x^2}. Note further that since the complete point expression is surrounded by round braces, round braces inside of x expression , y expression or z expression need to be treated specially. Surround the expressions (which contain round braces) with curly braces: \addplot3 ({ x expr }, { y expr }, { z expr });

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4.6.3

Line Plots

Three dimensional line plots are generated if the input source has no matrix structure. Line plots take the input coordinates and connect them in the order of appearance.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.2 0.4 0.6 0.8 x 0.5 1 0 y

If there is no value for neither mesh/rows nor mesh/cols or if one of them is 1, pgfplots will draw a line plot. This is also the case if there is no endofscanline marker (empty line) in the input stream. For \addplot3 expression, this requires to set samples y=0 to disable the generation of a mesh.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example above is a parametric plot by expression, i.e. it has three distinct expressions for x, y , and z . Line plots in three dimensions are also possible for data plots (tables). The most simple case is if you simply provide a series of threedimensional coordinates which will be connected in the order of appearance:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

Note that this plot implicitly has mesh/rows=1 because it has no endofscanline markers (empty lines). If in doubt, you can set mesh/rows=1 explicitly to tell pgfplots that you have onedimensional data (and not a matrix). Line plots from data les are also possible if the data les only contains two coordinates and the third should be provided somehow. In this case, the table/x expr feature comes into play: it allows to combine data plots and math expressions:

Here, we have two plots in one axis: one data plot from a data table with just two coordinates and one parametric plot. Both denote the same two functions. For the data plot, x expr=4 assigns the x coordinate, and y=a,z=b dene how the input columns map to coordinates. Again, the plot implicitly uses mesh/rows=1 since there is no endofscanline marker. The second plot does the same with the short handed notation (5,x,x^2). It only samples onedimensional data due to samples y=0. Finally, extra x ticks congures two additional ticks for the x axis; this is used to display grid lines for these specic ticks. The xticklabel=\empty argument avoids overprinted x tick labels at positions x {4, 5}. Three dimensional line plots will usually employ lines to connect points (i.e. the initial sharp plot handler of Tik Z). The smooth method of Tik Z might also prove be an option. Note that no piecewise constant plot, comb or bar plot handler is supported for three dimensional axes.

4.6.4

Scatter Plots

Three dimensional scatter plots have the same interface as for two dimensional scatter plots, so all examples of Section 4.5.10 can be used for the three dimensional case as well. The key features are to use only marks and/or scatter as plot styles. We provide some more examples which are specic for the three dimensional case. Our rst example uses only marks to place the current plot mark at each input position: A Scatter Plot Example% Preamble: \pgfplotsset{width=7cm,compat=1.9}

We used z filter to x the z coordinate to 1.4. We could also have used the table/z expr=1.4 feature\addplot3[scatter,scatter src=\thisrow{f(x)},only marks] table[z expr=1.4] {plotdata/pgfplotsexample4_grid.dat};

to get exactly the same eect. Choose whatever you like best. The z filter works for every coordinate input routine, the z expr feature is only available for plot table. The following example uses mark=cube* and z buffer=sort to place boxes at each input coordinate. The color for each box is determined by point meta={x+y+3}. The remaining keys are just for pretty

CHAPTER 4. THE REFERENCE

A mesh plot uses dierent colors for each mesh segment. The color is determined using a color coordinate which is also called meta data throughout this document. It is the same data which is used for surface and scatter plots as well, see Section 4.8. In the initial conguration, the color coordinate is the z axis (or the y axis for two dimensional plots). This color coordinate is mapped linearly into the current color map to determine the color for each mesh segment. Thus, if the smallest occurring color data is, say, 1 and the largest is 42, points with color data 1 will get the color at the lower end of the color map and points with color data 42 the color of the upper end of the color map.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The ll color needs to be provided explicitly. Details:

A mesh plot uses the same implementation as shader=flat to get one color for each single segment. Thus, if shader=flat mean, the color for a segment is determined using the mean of the color data of adjacent vertices. If shader=flat corner, the color of a segment is the color of one adjacent vertex. As soon as mesh is activated, color=mapped color is installed. This is necessary unless one needs a dierent color but mapped color is the only color which reects the color data. It is possible to use a dierent color using the color= color name as for any other plot. It is easily possible to add mark= marker name to mesh plots, scatter is also possible. Scatter plots will use the same color data as for the mesh.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Allows to congure whether an error is generated if mesh/rows mesh/cols does not equal the total number of coordinates.

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CHAPTER 4. THE REFERENCE If you know exactly what you are doing, it may be useful to disable the check. If you are unsure, it is best to leave the initial setting.

/pgfplots/z buffer=default|none|auto|sort|reverse x seq|reverse y seq|reverse xy seq (initially default) This key allows to choose between dierent z buering strategies. A z buer determines which parts of an image should be drawn in front of other parts. Since both, the graphics packages pgf and the nal document format .pdf are inherently two dimensional, this work has to be done in TEX. Currently, several (fast) heuristics can be used which work reasonably well for simple mesh- and surface plots. Furthermore, there is a (time consuming) sorting method which also works if the fast heuristics fails. The z buering algorithms of pgfplots apply only to a single \addplot command. Dierent \addplot commands will be drawn on top of each other, in the order of appearance. The choice default checks if we are currently working with a mesh or surface plot and uses auto in this case. If not, it sets z buffer=none. The choice none disables z buering. This is also the case for two dimensional axes which dont need z buering. The choice auto is the initial value for any mesh or surface plot: it uses a very fast heuristics to decide how to execute z buering for mesh and surface plots. The idea is to reverse either the sequence of all x coordinates, or those of all y coordinates, or both. For regular meshes, this suces to provide z buering. In other words: the choice auto will use one of the three reverse strategies reverse * seq (or none at all). The choice auto, applied to patch plots, uses z buffer=sort since patch plots have no matrix structure. The choice sort can be used for scatter, line, mesh, surface and patch plots. It sorts according to the depth of each point (or mesh segment). Sorting in TEX uses a slow algorithm and may require a lot of memory (although it has the expected runtime asymptotics O(N log N )). The depth of a mesh segment is just one number, currently determined as mean over the vertex depths. Since z buffer=sort is actually just a more intelligent way of drawing mesh segments on top of each other, it may still fail. Failure can occur if mesh segments are large and overlap at dierent parts of the segment (see Wikipedia Painters algorithm). If you experience problems of this sort, consider reducing the mesh width (the mesh element size) such that they can be sorted independently (for example automatically using patch refines=2, see the patchplots library). The remaining choices apply only to mesh/surface plots (i.e. for matrix data) and do nothing more then their name indicates: they reverse the coordinate sequences of the input matrix (using quasi linear runtime). They should only be used in conjunction by z buffer=auto.

4.6.6

Surface Plots(no value)

/pgfplots/surf \addplot+[surf]

A surface plot visualizes a two dimensional, single patch using dierent ll colors for each patch segment. Each patch segment is a (pseudo) rectangle, that means input data is given in form of a data matrix as is discussed in the introductory section about three dimensional coordinates, 4.6.2.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

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The simplest way to generate surface plots is to use the plot expression feature, but as discussed in Section 4.6.2 other input methods like \addplot3 table or \addplot3 coordinates are also possible. The appearance can be congured using colormaps, the value of the shader, faceted color keys and the current color and/or draw/fill color. As for mesh plots, the special color=mapped color is installed for the faces. The stroking color for faceted plots can be set with faceted color (see below for details).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.5 1 0.5 1.5 2 0

Details about the shading algorithm are provided below in the documentation of shader. Surface plots use the mesh legend style to create legend images. /pgfplots/shader=flat|interp|faceted|flat corner|flat mean|faceted interp The simplest choice is to use one ll color for each segment, the choice flat.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(initially faceted)

Congures the shader used for surface plots. The shader determines how the color data available at each single vertex is used to ll the surface patch.

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

There are (currently) two possibilities to determine the single color for every segment: flat corner Uses the color data of one vertex to color the segment. It is not dened which vertex is used here21 . flat mean Uses the mean of all four color data values as segment color. This is the initial value as it provides symmetric colors for symmetric functions. The choice flat is actually the same as flat mean. Please note that shader=flat mean and shader=flat corner also inuence mesh plots the choices determine the mesh segment color.21 pgfplots

just uses the last vertex encountered in its internal processings but after any z buer re-orderings.

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Another choice is shader=interp which uses Goraud shading (smooth linear interpolation of two triangles approximating rectangles) to ll the segments.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

The shader=interp employs a lowlevel shading implementation which is currently available for the following drivers: the postscript driver \def\pgfsysdriver{pgfsys-dvips.def}, the pdflatex driver \def\pgfsysdriver{pgfsys-pdftex.def}, the lualatex driver \def\pgfsysdriver{pgfsys-pdftex.def} (yes, it is the same), the dvipdfmx driver \def\pgfsysdriver{pgfsys-dvipdfmx.def}.

For other drivers, the choice shader=interp will result in a warning and is equivalent to shader=flat mean. See also below for detail remarks. Note that shader=interp,patch type=bilinear allows real bilinear interpolation, see the patchplots library. The choice shader=faceted uses a constant ll color for every mesh segment (as for flat) and the value of the key /pgfplots/faceted color to draw the connecting mesh elements:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

The last choice is shader=faceted interp. As the name suggests, it is a mixture of interp and faceted in the sense that each element is shaded using linear triangle interpolation (see also the patchplots library for bilinear interpolation) in the same way as for interp, but additionally, the edges are colored in faceted color:

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% Preamble: \pgfplotsset{width=7cm,compat=1.9}

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

In principle, there is nothing wrong with the idea as such, and it looks quite good but it enlarges the resulting pdf document considerably and might take a long time to render. It works as follows: for every mesh element (either triangle for patch plots or rectangle for lattice plots), it creates a low level shading. It then lls the single mesh element with that shading, and strokes the edges with faceted color. The declaration of that many low level shadings is rather inecient in terms of pdf objects (large output les) and might render slowly22 . For orthogonal plots (like view={0}{90}), the eect of faceted interp can be gained with less cost if one uses two separate \addplot commands: one with surf and one with mesh. Handle this choice with care. Details: All shaders support z buffer=sort (starting with version 1.4) The choice shader=faceted is the same as shader=flat except that it uses a special draw color. So, shader=faceted has the same eect as shader=flat,draw=\pgfkeysvalueof{/pgfplots/faceted color}. The flat shader uses the current draw and fill colors. They are set with color=mapped color and can be overruled with draw= draw color and fill= ll color . The mapped color always contains the color of the color map. You easily add mark= plot mark to mesh and/or surface plots or even colored plot marks with scatter. The scatter plot feature will use the same color data as for the surface. But: Markers and surfaces do not share the same depth information. They are drawn on top of each other. Remarks on shader=interp:

It uses the current color map in any case, ignoring draw and fill. For surface plots with lots of points, shader=interp produces smaller pdf documents, requires less compilation time in TEX and requires less time to display in Acrobat Reader than shader=flat. The postscript driver truncates coordinates to 24 bit which might result in a loss of precision (the truncation is not very intelligent). See the surf shading/precision key for details. To improve compatibility, this 24 bit truncation algorithm is enabled by default also for pdf documents. The choice shader=interp works well with either Acrobat Reader or recent versions of free viewers23 . However, some free viewers show colors incorrectly (like evince). I hope this message will soon become outdated... if not, provide bug reports to the Linux community to communicate the need to improve support for Type 4 (patch) and Type 5 pdf (surf) and Type 7 (patch and elements of the patchplots library) shadings. The interp shader yields the same outcome as faceted interp,faceted color=none, although faceted interp requires much more ressources.22 My experience is as follows: Acrobat reader can eciently render huge interp shadings. But it is very slow for faceted interp shadings. Linux viewers like xpdf are reasonably ecient for interp (at least with my bugxes to libpoppler) and are also fast for faceted interp shadings. 23 The author of this package has submitted bugxes to xpdf/libpoppler which should be part of the current stable versions of many viewers.

1 0.5 0 0 1 0.2 0.4 0.6 0.8 0.5 1 0

/pgfplots/faceted color={ color name } Denes the color to be used for meshes of faceted surface plots. Set faceted color=none to disable edge colors.

(initially mapped color!80!black)

/pgfplots/mesh/interior colormap={ map name }{ colormap specication } /pgfplots/mesh/interior colormap name={ map name } Allows to use a dierent colormap for the other side of the surface. Each mesh has two sides: one which points to the views origin and one which points away from it. This key allows to dene a second colormap for the side which points away from the views origin. The motivation is to distinguish between the outer side and the interior parts of a surface:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The interior colormap is often the one for the inner side. However, the orientation of the surface depends on its normal vectors: pgfplots computes them using the right-hand-rule. The right-handrule applied to a triangle means to take the rst encountered point, point the thumb in direction of the

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CHAPTER 4. THE REFERENCE second point and the rst nger in direction of the third point. Then, the normal for that triangle is the third nger (i.e. the crossproduct of the involved oriented edges). For rectangular patches, pgfplots uses the normal of one of its triangles24 . Consequently, mesh/interior colormap will only work if the involved patch segments are consistently oriented. A patch whose normal vector points into the same direction as the view direction uses the standard colormap name. A patch whose normal vector points into the opposite direction (i.e. in direction of the viewport) uses mesh/interior colormap.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The implementation of mesh/interior colormap works well for most examples; in particular, if the number of samples is large enough to resolve the boundary between inner and outer colormap. However, it might still produce spurious artifacts: Example needing ne-tuning% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The previous example has need for improvement with respect to a couple of aspects: rst, it has small overshoots near some of the meshes vertices (especially on top of the hills). These can be xed using miter limit=1. Second, the boundary between blue and black is incorrect. This can be improved by means of an increased sampling density (samples=31). In addition, we can congure pgfplots to move the boundary between the two colormaps in favor of the blue region using mesh/interior colormap thresh as follows:24 This

This improves the display. Call for volunteers: it would be nice if the netuning of these keys would be unnecessary. If someone has wellfounded suggestions (like knowledge and perhaps exhaustive experiments) on how to improve the feature, let me know. Note that mesh/interior colormap cannot be combined with mesh/refines currently. Note that mesh/interior colormap will increase compilation times due to the computation of normal vectors. /pgfplots/mesh/interior colormap thresh={ Number between 1.0 and +1.0 } (initially 0)

A threshold which moves the boundary between the colormap and interior colormap in favor of colormap (if the value is negative) or in favor of interior colormap (if the value is positive).

A key to congure how the low level driver for shader=interp writes its data. The choice pdf uses 32 bit binary coordinates (which is lossless). The resulting .pdf les appear to be correct, but they cant be converted to postscript the converter software always complains about an error. The choice postscript (or, in short, ps) uses 24 bit truncated binary coordinates. This results in both, readable .ps and .pdf les. However, the truncation is lossy.

If anyone has ideas how to x this problem: let me know. As far as I know, Postscript should accept 32 bit coordinates, so it might be a mistake in the shading driver.

4.6.7

Surface Plots with Explicit Color

The surface plots described in Section 4.6.6 are all based on colormaps. This section introduces a dierent type of surface plot. In fact, it uses the very same plot handlers: it applies to mesh, surf, and patch plots. However, the way colors are provided and the way pgfplots interpolates colors is substantially dierent. This section describes surface plots with explicit colors. These expect colors like red, green, or rgb=(0.5,0.2,1) for every vertex of the mesh and interpolates smoothly between these vertices. This appears to be simpler, perhaps even more straight-forward than surface plots based on colormaps. It is not. Surface plots with explicit color are more dicult to dene, and they are more dicult to read. If you are in doubt of whether to use a surface colored by a colormap or explicit colors, you should prefer colormaps for reasons discussed below. /pgfplots/mesh/color input=colormap|explicit|explicit mathparse (initially colormap)

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CHAPTER 4. THE REFERENCE Allows to congure how pgfplots expects color input for surface plots. The choice colormap uses the standard colormaps. This particular choice expects scalar values of point meta which are mapped linearly into the colormap. It resembles the surface plots which are explained in more detail in Section 4.6.6. It is the default conguration and covers (probably) most common usecases. The choice explicit expects explicitly provided point meta of symbolic form: every coordinate of your input coordinate stream is supposed to have an explicitly dened color as point meta. Here, explicitly provided refers to point meta=explicit symbolic. This choice and the available color formats are explained in all detail in the following subsections. The choice explicit mathparse is similar to explicit, but it allows to provide just one math expression which is evaluated for every coordinate. The math expression can be of the form rgb=x,y,0.5 in which case x is used to dene the red component, y is used to dene the green component and the blue component is xed to 0.5. This key is also explained in more detail in the following subsections. The main usecase of mesh/color input=colormap is to allow a map between the interpolated colors and some value of interest. This map can be shown as colorbar:1 1 0.8 0.6 0.4 0.2 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that the preceding example is a standard surf plot except for patch type=bilinear which controls how color is to be interpolated. There is a 2 2 matrix, and its z values are used as color data. Clearly, value z = 0 corresponds to blue and z = 1 corresponds to red and all other colors inbetween are not directly related to blue and red; they are taken from the colormap. The colormap denes which colors appear: those which make up the colormap and those which can occur as interpolated colors between the colors of the color map. The pairwise mixture of colors is a property of mesh/color input=colormap, not of mesh/color input=explicit (where more than two colors are mixed together). Furthermore, the surface indicates contours of constant z level. Take, for example, the yellow contour. We know that it has some value between 0.3 and 0.4, say 0.35. Since these shadings are continuous, we know that the point z = 0.35 occurs between z = 0 and z = 1 at every point of the surface. Due to the colormap, each point on the surface which has z = 0.35 will receive the yellow color. This is because the interpolation is carried out on the scalar point meta value, which is afterwards mapped into the colormap. This contourproperty is also unique for colormap surfaces. The other two choices are explained in all detail in the next subsections. Providing Colors Explicitly For Each Coordinate Here is a simple approach with the same vertices as the colormapexample above, but with explicit colors:

The coordinates and the view is the same, even the way colors are being interpolated bilinearly. However, we have four dierent colors in the corners. We see these corners in the output, and we see that they are smoothly mixed together. However, the mix contains all four colors, not just two. As a direct consequence, there are no contour lines. The absence of direct information how to map color information to some information of the data visualization implies that if you want to use surface plots with explicit color, you have to state clearly what you want to show. This is considerably simpler for colormaps. The following example congures z = 0 to receive blue and z = 1 to receive red as in our preceding colormap example (see above) using mesh/color input=explicit.1 0 .8 0 .6 0 .4 0 .2 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

We see the bilinear nature of the interpolation; it is related to that of mesh/color input=colormap above (compare the contour lines inbetween). In most cases, you simply want to show some contour lines. And for such cases, a colormap is the way to go. There might be cases where mesh/color input=explicit is adequate. However, you will need to think it through properly. And you need to explain clearly what you did because your audience will also have to think a lot before they make sense of any data visualization based on explicit color interpolation. The choice mesh/color input=explicit expects a choice of point meta which results in symbolic values. In this context, symbolic refers to a special color denition:

The previous example denes a patch plot with three triangle patches, each made up of three vertices which are placed asis into the input coordinate stream. Each vertex has its color data in column c. The format of color specications is explained in more detail in the following paragraph. As soon as you write mesh/color input=explicit, pgfplots checks the current value of point meta. If the current value of point meta is none, it is set to point meta=explicit symbolic (that is what happened in our example above). If the current value of point meta is some choice which yields numeric output (like point meta=x or point meta=\thisrow{x}+1), it is set to point meta=explicit symbolic. If the current value of point meta is already of symbolic form, it is left unchanged. Consequently, our example above sets point meta=explicit symbolic as soon as it encounters mesh/color input=explicit. The explicit symbolic input handler in turn expects the coordinate stream to provide point meta data for every streamed coordinate. We use a table here, and a table reads its color data from the column name provided in the table/meta key. The accepted format of colors is quite similar to that of Colormap denitions (compare Section 4.7.6 on page 166). The common format is color model = arguments . In contrast to the similar input format inside of colormap denitions, the syntax here has no round braces and does not have the length argument. Nevertheless, the same color model s with the same arguments are accepted. The choices are rgb= red , green , blue where each component is in the interval [0, 1], rgb255= red , green , blue is similar to rgb except that each component is expected in the interval [0,255], gray= value with value in the interval [0, 1], color= named color where named color is a predened (named) color like red or a color expression like red!50, cmyk= cyan , magenta , yellow , black where each component is in the interval [0, 1], cmyk255= cyan , magenta , yellow , black is the same as cmyk but expects components in the interval [0, 255], cmy= cyan , magenta , yellow where each component is in the interval [0, 1], hsb= hue , saturation , brightness where each component is in the interval [0, 1], Hsb= hue , saturation , brightness is the same as hsb except that hue is accepted in the interval [0, 360] (degree), HTML= hex red hex green hex blue where component is expected to be a hex number between 00 and FF (a variant of rgb255), wave= wave length which expects a single wave length as numeric argument in the range [363, 814].

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/pgfplots/mesh/colorspace explicit color input=rgb|rgb255|cmy|cmyk|cmyk255|gray|wave|hsb |Hsb|HTML (initially rgb) If the input color has no color model, the color components are interpreted as color in the color model specied as argument to this key. This key has just one purpose: to omit the color model if it is the same for lots of points anyway. /pgfplots/mesh/colorspace explicit color output=rgb|cmyk|gray (initially rgb)

Any color which is encountered by the survey phase (i.e. while inspecting the point meta value) is immediately transformed into the color space congured as mesh/colorspace explicit color output. Note that this option has no eect if you told xcolor to override the color space globally. More precisely, the use of\usepackage[cmyk]{xcolor}

or, alternatively,\selectcolormodel{cmyk}

will cause all colors to be converted to cmyk, and pgfplots honors this conguration. Consequently, both these statements cause all colors to be interpolated in the desired color space, and all output colors will use this colorspace. This is typically exactly what you need. The transformed color is used for any color interpolation. In most cases, this is done by the shader, but it applies to patch refines and patch to triangles as well. Because the transformed color is used for color interpolation, the list of available output color spaces is considerably smaller than the available input color spaces. Only the device color spaces rgb, gray, and cmyk are available as value for mesh/colorspace explicit color output. Any necessary colorspace transformations rely on the xcolor package25 . Note that colorspace transformations are subject to nearestcolormatching, i.e. they are less accurate. This is typically far beyond pure rounding issues; it is caused by the fact that these color spaces are actually so dierent that transformations are hard to accomplish. If you can specify colors immediately in the correct color space, you can eliminate such transformations. Here is the same shading, once with CMYK output and once with RGB output. Depending on your output media (screen or paper), you will observe slightly dierent colors when comparing the pictures. RGB shading 4% Preamble: \pgfplotsset{width=7cm,compat=1.9}

This key is similar to the related key colormap default colorspace, although the values can be chosen independently. Providing Color Components as Table The previous section shows how to provide a single symbolic color expression for each coordinate, namely using point meta=explicit symbolic. Another usecase might be to provide a table containing both the coordinate values and one column by color component. In order to assemble the color specication from the input table, you can provide a symbolic expression: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example employs a patch plot with triangular elements as we have seen before. Furthermore, it uses explicit color input but combined with point meta={symbolic={ value }} (note the extra pair of braces). This choice accepts arbitrary symbols on input which will be reevaluated (expanded) for every coordinate. In our example, we simply read the values from table columns using \thisrow. Since the default input colorspace is RGB, this results in the expected triangle with red, green, and blue corners. The result has to form a valid color specication. Note that the symbolic expression is purely stringbased in this context. If you plan to use math expressions, you have to use mesh/color input=explicit mathparse as explained in the following section. Providing Colors as Math Expression The key mesh/color input has two choices for explicit color input. The choice explicit has been discussed in the preceding paragraphs, it expects one color specication for every node for which colors are needed. It also accepts a kind of stringbased expressions to concatenate the expected color specication in a suitable way.

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The second choice mesh/color input=explicit mathparse is almost the same with one major difference: it allows to provide math expressions inside of the point meta value. However, the provided math expressions need to form a color specication which typically has more than one color component. With this choice, the value of point meta is of symbolic form, but the color components are reevaluated with the math parser for every input point which has color data. The most convenient way to provide such expressions is point meta={symbolic={ R , G , B }} (again, note the extra set of braces for the argument). 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example is a surface plot with a 2 2 input matrix. Note that the table has no explicit point meta data. The point meta data is acquired from a common math expression which uses the nal x coordinate as red component, the value seen in the current row and column y as green value and constant value blue = 0. Consequently, the output is black in the lower left corner since black is (0, 0, 0), red in the lower right corner, green in the upper left corner, and a mixture of both along the diagonal. The value provided as point meta={symbolic={ value }} is of the same form as for mesh/color input=explicit, i.e. it is supposed to be of the form color model = color components . If the color model is omitted, it defaults to mesh/colorspace explicit color input (which is rgb by default). Since the math expression can be anything, it can safely be combined with plot by expression. A potential usecase could be to show a surface with (x, y, z ) and some twodimensional quantity which is encoded as mixture of red and green. The following example relies on mesh/color input=explicit mathparse and point meta=symbolic to provide a vector of math expressions:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE Note that the preceding example suers from color burning26 : the green areas become too bright and the black areas become too dark. Note that the picture is entirely acceptable if it is written as standalone picture. But as soon as you import the picture (either as .pdf or as .png) into a document for which opacity is active, it suers from burned colors. The color burning is caused by the combination of RGB colorspace, the special color set in this example, and the color blending which is activated by opacity. Note that it is enough to activate opacity somewhere in the document. In order to repair the problem for the picture at hand, one has to choose a dierent output colorspace:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The key mesh/colorspace explicit color output transforms every input RGB color to a matching CMYK color. This, in turn, is a lossy transformation which seems to lack a trivial solution27 . Math expressions can also be used for complicated input color spaces, for example the wave colorspace.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that you have to take care that the color components are within the expected bounds.

4.6.8

Contour Plots

pgfplots supports visualization of contour plots whose coordinates have been computed by external tools. The contour prepared plot handler coming with pgfplots takes precomputed contour line coordinates and handles their visualization (contour/draw color, contour/labels etc.). The contour gnuplot style takes matrix input in the same format as for mesh or surf (that includes any of the pgfplots matrix input methods). It then writes the matrix data to a le and invokes gnuplot (or other, user customizable external programs) to compute contour coordinates. Finally, the computed contours are visualized with the contour26 At 27 If

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prepared algorithm. Thus, external programs need to compute the contour coordinates and pgfplots visualizes the result. We discuss the high level interface to external programs rst and continue with contour prepared later-on. /pgfplots/contour gnuplot={ options with contour/ or contour external/ prex } \addplot+[contour gnuplot={ options with contour/ or contour external/ prex }] This is a high level contour plot interface. It expects matrix data in the same way as two dimensional surf or mesh plots do. It then computes contours and visualizes them. 420 2 100

The example uses \addplot3 together with expression plotting, that means the input data is of the form (xi , yi , f (xi , yi )). The view={0}{90} ag means view from top, otherwise the contour lines would have been drawn as z value:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

As mentioned, you can use any of the pgfplots input methods as long as it yields matrix output. Thus, we can re-use our introductory example of matrix data, this time with inline data: 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(0,1,0) (1,1,0.6) (2,1,0.7) (3,1,0.5)

0.5 0.5 1 1.5 2 2.5 3

CHAPTER 4. THE REFERENCE What happens behind the scenes is that pgfplots takes the input matrix and writes all encountered coordinates to a temporary le, including the endofscanline markers. Then, it generates a small gnuplot script and invokes gnuplot to compute the contour coordinates, writing everything into a temporary output le. Afterwards, it includes gnuplots output le just as if youd write \addplot3[contour prepared] file { temporaryle };. All this invocation of gnuplot, including input/output le management is transparent to the user. It only requires two things: rst of all, it requires matrix data as input28 . Second, it requires you to enable system calls. Consider the documentation for plot gnuplot for how to enable system calls. Note that the z coordinate of the data which is communicated to gnuplot is the current value of point meta. This allows to generate contours on two columns only and has more freedom. See also the contour external/output point meta key. The resulting data can be projected onto a separate slice, for example using z filter.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

An unexpected sideeect of a z filter combined with contour gnuplot is that the color information and the label sizes are essentially lost. To componsate this eect, we have to assign a new value for point meta. But since point meta denes the values for contour levels (see above), there is a special key named output point meta which can be used here:28 Note that contour gnuplot processes the input stream only once. Consequently, the temporary le will contain only information which was available before the rst point has been seen. The example above works because it contains emptylines as end-of-scanline markers. If you do not provide such markers, you may need to provide two of the three options mesh/rows, mesh/cols, or mesh/num points.

Here, output point meta=rawz allows to assign point meta to the output of the contouring algorith, i.e. something which is handed over to contour prepared. The choice rawz means to use the unltered z coordinate which is what we want here. There are several ne-tuning parameters of the input/output le management, and it is even possible to invoke dierent programs than gnuplot (even matlab). These details are discussed at the end of this section, see below at page 146. /pgfplots/contour/number={ integer } (initially 5)

Congures the number of contour lines which should be produced by any external contouring algorithm. x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

It is also possible to change the /pgf/number format settings, see the documentation for the contour/every contour label style below. Note that contour/number has no eect on contour prepared. /pgfplots/contour/levels={ list of levels } (initially empty)

Congures the number of contour lines which should be produced by any external contouring algorithm by means of a list of discrete levels.

It is also possible to change the /pgf/number format settings, see the documentation for the contour/every contour label style below. This key has higher precedence than contour/number, i.e. if both are given, contour/levels will be active. Note that contour/levels has no eect on contour prepared. /pgfplots/contour/contour dir=x|y|z x exp(x2 y 2 ) (initially z) Allows to generate contours with respect to another direction.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0.4 0.2 0 0.2 0.4 1 0 0 1 2 2

The input data is the same as before it has to be given in matrix form. The key contour dir congures the algorithm to compute contours along the provided direction. x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note, however, that each contour line receives a single color. This is what one expects for a contour plot: it has a single style, and a single contour level. Note furthermore that the color which is assigned to a contour plot with contour dir=x is dierent compared with the color assigned to a contour plot with contour dir=z: the argument of contour dir implicitly denes the argument for point meta (also known as color data). More precisely, a contour plot with contour dir=x has point meta=x whereas a contour plot with contour dir=z uses point meta=z. If you would like to have individually colored segments inside of contours, you have to use a dierent plot handler. There is a simple alternative which works well in many cases: you can use a standard mesh plot combined with patch type=line: x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we did not generate a contour plot. We generated a mesh plot with patch type=line. The choice patch type=line causes an inherently onedimensional plot as opposed to the default matrix style visualization which would be generated by mesh in dierent cases. Since a mesh plot uses one color for every patch segment, we have a lot of freedom to color the segments. In the example above, we have the default conguration point meta=z, i.e. the z value denes the color. The fact that a mesh plot with patch type=line yields almost the same output as contour dir=y is an artifact of the scanline encoding. Our example uses \addplot3 expression which relies on mesh/ordering=x varies. If we visualize the resulting matrix by means of patch type=line, the visualization follows the scanlines which vary along the x axis. In our example, we used samples y=10 to control the number of contour lines. A consequence of the previous paragraph is that we have a more challenging task at hand if we want to get the same eect as contour dir=x: we would need mesh/ordering=y varies. In our case, we would need to transpose the data matrix. For \addplot3 expression, this is relatively simple: we can exchange the meaning of x and y to get a transposition:

This is the same example as above but as you noted, the meaning of x and y in the expression has been exchanged and the notation has been switched to a parametric plot. Such an approach is also possible for data les, but pgfplots cannot transpose the matrix ordering on its own. Coming back to contour dir, we can also use its output to generate several contour projections using coordinate lters.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example uses a xed draw color combined with x filter, y filter, and z filter to x the contours in one of the axis planes. Technical background: This section is probably unnecessary and can be skipped. The key contour dir is implemented by means of coordinate permutations. Since contouring algorithms always support contour dir=z, it is relatively simple to compute z contour lines from input matrixes X, Y, Z . The choice contour dir=z key simply takes the input asis. The choice contour dir=x reorders the input coordinates to yzx. The choice contour dir=y reorders the input coordinates to xzy. All this reordering is applied before coordinates are handed over to the contouring algorithm (see contour external) and is undone when reading the results back from the contouring algorithm. That means that contour dir is also available for contour prepared. In this context, contour prepared is supposed to be the output of some contouring algorithm. Its input coordinates are automatically reordered according to the inverse permutation. This allows to draw x or y contours which are given in the prepared format.

A plot handler which expects already computed contours on input and visualizes them. It cannot compute contours on its own. /pgfplots/contour prepared format=standard|matlab (initially standard) There are two accepted input formats. The rst is a long sequence of coordinates of the form (x, y, z ) where all successive coordinates with the same z value make up a contour level (this is only part of complete truth, see below). The endofscanline markers (empty lines in the input) mark an interruption in one contour level. For example, contour prepared format=standard could be29 2 1.5 1 0.5 10.40.2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that the empty lines are not necessary in this case: empty lines make only a dierence if they occur within the same contour level (i.e. if the same z value appears above and below of them). The choice contour prepared format=matlab expects twodimensional input data where the contour level and the number of elements of the contour line are provided as x and y coordinates, respectively, of a leading point. Such a format is used by matlabs contour algorithms, i.e. it resembles the output of the matlab commands data=contour(...) or data=contourc(...).29 This

is actually the output from our \addplot3[contour gnuplot] coordinates example from above.

In case you use matlab, you can generate such data with [x,y]=meshgrid(linspace(0,1,15)); data=contour(x,y,x.*y); data=data; save exporteddata.dat data -ASCII As already mentioned in the beginning, the z coordinate is not necessarily the coordinate used to delimit contour levels. In fact, the point meta data is acquired here, i.e. you are free to use whatever z coordinate you want as long as you have a correct point meta value. The example from above could be modied as follows:

The example above uses dierent z coordinates for each rst and each last point on contour lines. The contour lines as such are dened by the level column since we wrote point meta=\thisrow{level}. Such a feature also allows contour prepared for nonstandard axes, compare the examples for the ternary lib on page 421. /pgfplots/contour/draw color={ color } (initially mapped color)

Note that \pgfplotspointmetarangeexponent= e where m 10e is the largest occuring label value (technically, it is the largest occurring value of point meta). The following example modies the /pgf/number format styles for contour labels: x exp(x2 y 2 )% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/contour external={ options with contour/ or contour external/ prex } \addplot+[contour external={ options with contour/ or contour external/ prex }] This handler constitutes a generic interface to external programs to compute contour lines. The contour gnuplot method is actually a special case of contour external. /pgfplots/contour external/file={ base le name } The initial conguration is to automatically generate a unique le name. /pgfplots/contour external/scanline marks=false|if in input|required|true (initially if in input) Controls how contour external writes end-of-scanline markers. The choice false writes no such markers at all. In this case, script should contain mesh/rows and/or mesh/cols. The choice if in input generates end-of-scanline markers if they appear in the provided input data (either as empty lines or if the user provided at least two of the three options mesh/rows, mesh/cols, or mesh/num points explicitly). The choice required works like if in input, but it will fail unless there really was such a marker. The choice true is an alias for required. /pgfplots/contour external/script={ Code for external program } (initially empty) (initially empty)

Provides template code to generate a script for the external program. Inside of Code for external program , the placeholder \infile will expand to the temporary input le and \outfile to the temporary output le. The temporary \infile is a text le containing one point on each line, in the form x y meta meta, separated by tabstops. Whenever a scanline is complete, an empty line is issued (but only if these scanline markers are found in the input stream as well). The complete set of scanlines forms a matrix. There are no additional comments or extra characters in the le. The macro \ordering will expand to 0 if the matrix is stored in mesh/ordering=x varies and \ordering will be 1 for mesh/ordering=y varies. Inside of Code for external program , you can also use \pgfkeysvalueof{/pgfplots/mesh/rows} and \pgfkeysvalueof{/pgfplots/mesh/cols}; they expand to the matrix size. Similarly, \pgfkeysvalueof{/pgfplots/mesh/num points} expands to the total number of points. Inside of Code for external program , the macro \thecontournumber is dened to be the value \pgfkeysvalueof{/pgfplots/contour/number} and \thecontourlevels contains the value \pgfkeysvalueof{/pgfplots/contour/levels}. These two macros simplify conditional code. If you need one of the characters ["|;:#] and some macro package already uses the character for other purposes, you can prepend them with a backslash, i.e. write \" instead of ". /pgfplots/contour external/script extension={ extension } The le name extension for the temporary script. /pgfplots/contour external/cmd={ system call } (initially empty) (initially script)

A template to generate system calls for the external program. Inside of system call , you may use \script as placeholder for the lename which contains the result of contour external/script. /pgfplots/contour external/output point meta={ point meta read from result of external tool } (initially empty) Allows to customize the point meta conguration which is applied to the result of the external tool.

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CHAPTER 4. THE REFERENCE In contour external, the value of point meta is used to generate the input z coordinate for the external tool. As soon as the external tool computed contour lines, its output is read and interpreted as contour lines and the value of output point meta determines the value of point meta which will be used to visualize the result. An empty value means to use the z coordinate returned by the external tool. Any other value is interpreted as a valid choice of point meta. /pgfplots/contour gnuplot The initial conguration is\pgfplotsset{ contour gnuplot/.style={ contour external={ script={ unset surface; \ifx\thecontourlevels\empty set cntrparam levels \thecontournumber; \else set cntrparam levels discrete \thecontourlevels; \fi set contour; set table \"\outfile\"; splot \"\infile\"; }, cmd={gnuplot \"\script\"}, #1,% }, } }

(style, no value)

Note that contour gnuplot requires explicit scanline markers in the input stream, and it assumes mesh/ordering=x varies. Note that contour external lacks the intelligence to detect changes; it will always re-generate the output (unless the -shell-escape feature is not active).

4.6.9

Parameterized Plots

Parameterized plots use the same plot types as documented in the preceding sections: both mesh and surface plots are actually special parametrized plots where x and y are on cartesian grid points. Parameterized plots just need a special way to provide the coordinates:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example uses samples y=0 to indicate that a line shall be sampled instead of a matrix. The curly braces are necessary because TEX cant nest round braces. The single expressions here are used to parametrize the helix. Another example follows. Note that z buffer=sort is a necessary method here.

3D Quiver Plots (Arrows)

Three dimensional quiver plots are possible with the same interface as their two-dimensional counterparts, simply provide the third coordinate using quiver/w. Please refer to Section 4.5.7 for details and examples.

4.6.11

About 3D Const Plots and 3D Bar Plots

There are currently no equivalents of const plot and its variants or the bar plot types like ybar for three dimensional axes, sorry.

4.6.12

Patch Plots(no value)

/pgfplots/patch \addplot+[patch]

Patch plots are similar to mesh and surf plots in that they describe a lled area by means of a geometry. However, patch plots are dened by explicitly providing the elements of the geometry: they expect a sequence of triangles (or other patch types) which make up the mesh. There are two dimensional and three dimensional patch plots, both with the same interfaces which are explained in the following sections.

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The standard input format (constituted by mesh input=patches) is to provide a sequence of coordinates (either two or threedimensional) as usual. Each consecutive set of points makes up a patch element, which is often a triangle: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Patch plots use point meta to determine ll colors. In its initial conguration, point meta will be set to the y coordinate (or the z coordinate for three dimensional patch plots). Set point meta somehow to color the patches: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

2 0 1 3 1 0 4 0 0.5 }; \end{axis} \end{tikzpicture}

Patch plots make use of the mesh conguration, including the shader. Thus, the example above uses the initial shader=faceted (which uses the mean color data to determine a triangles color and a related stroke color). The shader=interp yields the following result:

CHAPTER 4. THE REFERENCE

2 0 1 3 1 0 4 0 0.5 }; \end{axis} \end{tikzpicture}

For triangles, shader=interp results in linearly interpolated point meta values throughout each individual triangle, which are then mapped to the color map (a technique also known as Gouraud shading). The color data does not need to be continuous, it is associated to triangle vertices. Thus, changing some of the color values allows individually shaded regions: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

2 0 0.5 3 1 1 4 0 0.5 }; \end{axis} \end{tikzpicture}

Two dimensional patch plots simply draw triangles in their order of appearance. In three dimensions, single elements are sorted according to their view depth, with foreground elements drawn on top of background elements (Painters algorithm, see z buffer=sort). /pgfplots/patch table={ table le name or inline table } (initially empty) /pgfplots/patch table with point meta={ table le name or inline table } (initially empty) /pgfplots/patch table with individual point meta={ table le name or inline table } (initially empty) Allows to provide patch connectivity data stored in an input table. A nonempty argument for patch table enables patch input mode. Now, the standard input stream is a long list of vertices which are stored in an array using their \coordindex as key. Each row of table le name or inline table makes up one patch, dened by indices into the vertex array:

The example consists of two separate tables. The patch table argument is a table, provided inline where rows are separated by \\ (which is the purpose of the row sep=\\ key as you guessed30 ). The patch table here declares three triangles: the triangle made up by vertex #0, #1 and #2, the triangle made up by #1, #2 and #3 and nally the one using the vertices #4, #3 and #5. The vertices as such are provided using the standard input methods of pgfplots; in our case using a table as well. The standard input simply provides coordinates (and point meta) which are stored in the vertex array; you could also have used plot coordinates to provide them (or plot expression). The argument to patch table needs to be a table either a le name or an inline table as in the example above. The rst n columns of this table are assumed to contain indices into the vertex array (which is made up using all vertices of the standard input as explained in the previous paragraph). The entries in this table can be provided in oating point, just make sure they are not rounded. The variable n is the number of vertices required to make up a single patch. For triangular patches, it is n = 3, for patch type=bilinear it is n = 4 and similar for other choices of patch type. The alternative patch table with point meta is almost the same as patch table but it allows to provide (a single) point meta (color data) per patch instead of per vertex. Here, a further column of the argument table is interpreted as color data: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The patch table with point meta always prefers point meta data from the provided table argument. However, it is still supported to write point meta=\thisrow{ colname } or similar constructs but now, colname refers to the provided table argument. More precisely, point meta is evaluated in a context where the patch connectivity has been resolved and the patch table with point meta is loaded.30 Note that the choice row sep=\\ is much more robust here: newlines would be converted to spaces by T X before pgfplots E had a chance to see them.

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CHAPTER 4. THE REFERENCE The other alternative patch table with individual point meta is very similar, but instead of a at color per patch, it allows to write one color value for every patch: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

To nd the point meta data for vertex #i, i = 0, 1, 2, pgfplots searches in column i + n where n is the number of vertices for patch type (in our case, n = 3). Technical remark: The key patch table with individual point meta automatically installs point meta=explicit as well. It might be confusing to override the value of point meta here (although it is allowed). The patch table input type allows to reduce the size of geometries since vertices are stored just once. pgfplots unpacks them into memory into the redundant format in order to work with single patch elements31 . In case you experience TEX memory problems with this connectivity input, consider using the redundant format. It uses other types of memory limits. A more involved example is shown below; it uses \addplot3[patch] to visualize a three dimensional patch plot, provided by means of a long sequence of patches:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The ordering in which triangles are specied is irrelevant, threedimensional patch plots use z buffer=sort to sort patches according to their depth (dened as mean depth over each vertex), where foreground patches are drawn on top of background patches. This socalled Painters algorithm works well for most meshes. If it fails, consider using patch refines=1 or patch refines=2 to split larger elements into small ones automatically.31 The reason for such an approach is that T X doesnt really know what an array is and according to my experience, arrays E implemented by macros tend to blow up TEXs memory limits even faster than the alternative.

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The drawing color associated to single vertices can be changed using the point meta key (which is the common method to congure color data in pgfplots). The initial conguration is point meta=z for three dimensional patch plots, i.e. to use the z coordinate also as color data. Use point meta=\thisrow{ colname } in conjunction with \addplot3[patch] table to load a selected table column. Patch plots are (almost) the same as mesh or surf plots, they only have more freedom in their input format (and a more complicated geometry). Actually, patch is just a style for surf,mesh input=patches. In other words, patch is the same as surf, it even shares the same internal implementation. Thus, most of the keys to congure mesh or surf plots apply to patch as well, especially shader and z buffer. As already mentioned, \addplot3[patch] automatically activates z buffer=sort to ensure a good drawing sequence. The shader can be used to modify the appearance:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

See the description of shader=interp for details and remarks. The example above makes use of the alternative syntax to provide a geometry: the patch table input. It allows to provide vertices separate from patch connectivity, where each patch is dened using three indices into the vertex array as discussed above.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

154 /pgfplots/mesh input=lattice|patches

CHAPTER 4. THE REFERENCE

This key controls how input coordinates are decoded to get patches. It is used only if patch table is empty (patch table has its own way to decode input coordinates). Usually, you wont need to bother with this key as it is set implicitly. The choice mesh input=lattice is the initial conguration for mesh and surf plots: it expects input in a compact matrix form as described at the beginning of this section starting with page 109 and requires a mesh/ordering and perhaps endofscanline markers. It yields patches with exactly four corners and is compatible with patch type=rectangle and patch type=bilinear (the latter requiring to load the patchplots library). The choice mesh input=patches is implicitly set when you use the patch style (remember that surf is actually some sort of patch plot on its own). It expects the input format as described for patch plots, i.e. n consecutive coordinates make up the vertices of a single patch where n is the expected number of vertices for the congured patch type. Note that a nonempty patch table implies mesh input=patches.

The initial conguration patch type=default checks the conguration of mesh input: for mesh input=patches, it uses triangle. For mesh input=lattice, it checks if there is just one row or just one col and uses patch type=line in such a case, otherwise it uses patch type=rectangle. The choice patch type=rectangle expects n = 4 vertices. The vertices can be either encoded as a matrix or, using mesh input=patches, in the sequence in which you would connect the vertices: Rectangle from matrix input 1 (2) (3)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(0) 0 0.2 0.4 0.6 0.8

(1) 1

As for all other patch type values, the vertices can be arbitrary two or threedimensional points, there may be even two on top of each other (resulting in a triangle). When used together with shader=interp, patch type=rectangle is visualized using two Gouraud shaded triangles (see

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155

below for triangle). It is the most ecient representation for interpolated shadings together with mesh input=lattice since the input lattice is written directly into the pdf. Use patch type=rectangle if you want rectangular elements and perhaps some sort of smooth shading. Use patch type=bilinear of the patchplots library in case you need real bilinear shading. Examples of such shadings can be found in Section 5.6.1. The choice patch type=triangle expects n = 3 vertices which make up a triangle. The ordering of the vertices is irrelevant: (2)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(0) 0 0.2 0.4 0.6 0.8

(1) 1

The use of shader=interp is implemented by means of linear interpolation of the three color values (specied with the point meta key) between the corners; the resulting interpolated point meta values are then mapped into the actual colormap. This type of interpolation is called Gouraud shading. Examples of such shadings can be found in Section 5.6.1. The choice patch type=line expects n = 2 vertices which make up a line. It is used for onedimensional mesh plots (see Section 4.5.11 for examples). There are more values for patch type like bilinear, triangle quadr, biquadratic, coons, polygon and tensor bezier. Please refer to the separate patchplots library in Section 5.6. /pgfplots/every patch This style will be installed as soon as the patch plot handler is activated. The initial conguration is\pgfplotsset{ every patch/.style={miter limit=1} }

(style, no value)

which improves display of sharp triangle corners signicantly (see the Tik Z manual for details about miter limit and line join parameters). There is much more to say about patch plots, like patch type which allows triangles, bilinear elements, quadratic triangles, biquadratic quadrilaterals, coons patches; the patch refines key which allows automatic renement, patch to triangles which triangulates higher order elements; how matrix data can be used for rectangular shapes and more. These details are subject of the patchplots library in Section 5.6.

CHAPTER 4. THE REFERENCE

4.7. MARKERS, LINESTYLES, (BACKGROUND-) COLORS AND COLORMAPS

mark=halfcircle* One half is lled with white (more precisely, with mark color) and the other half is lled with the actual fill color. mark=pentagon mark=pentagon* mark=text p p p p

This marker is special as it can be congured freely. The character (or even text) used is congured by a set of variables, see below. mark=cube

This marker is only available inside of a pgfplots axis, it draws a cube with axis parallel faces. Its dimensions can be congured separately, see below. mark=cube*

User defined It is possible to dene new markers with \pgfdeclareplotmark, see below. All these options have been drawn with the additional options\draw[ gray, thin, mark options={% scale=2,fill=yellow!80!black,draw=black } ]

Please see Section 4.7.5 for how to change draw and fill colors. Note that each of the provided marks can be rotated freely by means of mark options={rotate=90} or every mark/.append style={rotate=90}. /tikz/mark size={ dimension } (initially 2pt)

A key which overrides any mark value set by cycle list of option lists after \addplot. If this style is provided as argument to a complete axis, it is appended to every axis plot post such that it disables markers even for cycle lists which contain markers. /tikz/mark repeat={ integer } Allows to draw only each nth mark where n is provided as integer . /tikz/mark phase={ integer p } (initially 1) (initially empty)

This option allows to control which markers are drawn. It is primarily used together with the Tik Z option mark repeat=r: it tells Tik Z that the rst mark to be draw should be the pth, followed by the (p + r)th, then the (p + 2r)th, and so on.1 0.5 0 0.5 1 6 4 2 0 2 4 6 1 0.5 0 0.5 1 6 4 2 0 2 4 6 % Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, p = 1 is the rst point (the one with \coordindex= 0).

159 (initially empty)

(initially empty)

Denes the additional ll color for the halfcircle, halfcircle*, halfdiamond* and halfsquare* markers. An empty value uses white (which is the initial conguration). The value none disables lling for this part. These markers have two distinct ll colors, one is determined by fill as for any other marker and the other one is mark color. 1 0.5 0 2 1 0 1 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

There is no limitation about the number of characters or whatever. In fact, any TEX material can be inserted as text , including images. /pgf/text mark style={ options for mark=text } Denes a set of options which control the appearance of mark=text. If /pgf/text mark as node=false (the default), options is provided as argument to \pgftext which provides only some basic keys like left, right, top, bottom, base and rotate. If /pgf/text mark as node=true, options is provided as argument to \node. This means you can provide a very powerful set of options including anchor, scale, fill, draw, rounded corners etc. /pgf/text mark as node=true|false (initially false)

Congures how mark=text will be drawn: either as \node or as \pgftext.

The rst choice is highly exible and possibly slow, the second is very fast and usually enough. \pgfdeclareplotmark{ plot mark name }{ code } Denes a new marker named plot mark name . Whenever it is used, code will be invoked. It is supposed to contain (preferrable pgf basic level) drawing commands. During code , the coordinate systems origin denotes the coordinate where the marker shall be placed. Please refer to [5] section Mark Plot Handler for more detailed information. /pgfplots/every axis plot post (style, initially )

The every axis plot post style can be used to overwrite parts (or all) of the drawing styles which are assigned for plots.

Markers paths are not subjected to clipping as other parts of the gure. Markers are either drawn completely or not at all. Tik Z oers more options for marker ne tuning, please refer to [5] for details.

4.7.2

Line Styles(style, no value)

The following line styles are predened in Tik Z. /tikz/solid

/tikz/dotted

(style, no value)

/tikz/densely dotted

(style, no value)

/tikz/loosely dotted

(style, no value)

/tikz/dashed

(style, no value)

/tikz/densely dashed

(style, no value)

/tikz/loosely dashed

(style, no value)

/tikz/dashdotted

(style, no value)

/tikz/densely dashdotted

(style, no value)

/tikz/loosely dashdotted

(style, no value)

/tikz/dashdotdotted

(style, no value)

/tikz/densely dashdotdotted

(style, no value)

/tikz/loosely dashdotdotted

(style, no value)

4.7. MARKERS, LINESTYLES, (BACKGROUND-) COLORS AND COLORMAPS since these styles apply to markers as well, you may want to consider using\pgfplotsset{ every mark/.append style={solid} }

Edges and Their Parameters

When pgfplots connects points, it relies on pgf drawing parameters to create proper edges (and it only changes them in the every patch style). It might occasionally be necessary to change these parameters: /tikz/line cap=round|rect|butt (initially butt) /tikz/line join=round|bevel|miter (initially miter) /tikz/miter limit= factor (initially 10) These keys control how lines are joined at edges. Their description is beyond the scope of this manual, so interested readers should consult [5]. Here is just an example illustrating why it might be of interest to study these parameters: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0)}; 0)}; 0)}; 0)};

Font Size and Line Width

Often, one wants to change line width and font sizes for plots. This can be done using the following options of Tik Z. /tikz/font={ font name } (initially \normalfont)

Sets the font which is to be used for text in nodes (like tick labels, legends or descriptions).A A font can be any L TEX argument like \footnotesize or \small\bfseries32 .

0.532 ConT

It may be useful to change fonts only for specic axis descriptions, for example using\pgfplotsset{ tick label style={font=\small}, label style={font=\small}, legend style={font=\footnotesize} }

See also the predened styles normalsize, small and footnotesize in Section 4.10.2.EXt and plain TEX users need to provide other statements, of course.

162 /tikz/line width={ dimension }

CHAPTER 4. THE REFERENCE (initially 0.4pt)

Sets the line width. Please note that line widths for tick lines and grid lines are predened, so it may be necessary to override the styles every tick and every axis grid. The line width key is changed quite often in Tik Z. You should use\pgfplotsset{every axis/.append style={line width=1pt}}

or\pgfplotsset{every axis/.append style={thick}}

to change the overall line width. To also adjust ticks and grid lines, one can use\pgfplotsset{every axis/.append style={ line width=1pt, tick style={line width=0.6pt}}}

The preceding example denes data which is used a couple of times throughout this manual; it is referenced by \plotcoords.101 102 L2 Error 103 104 105 d=2 d=3 d=4 d=5 d=6% Preamble: \pgfplotsset{width=7cm,compat=1.9}

pgf uses the color support of xcolor. Therefore, the main reference for how to specify colors is the xcolor manual [3]. The pgf manual [5] is the reference for how to select colors for specic purposes like drawing, lling, shading, patterns etc. This section contains a short overview over the specication of colors in [3] (which is not limited to pgfplots).

red!30!white Besides predened colors, it is possible to mix two (or more) colors. For example, contains 30% of red and 70% of white. Consequently, one can build red!70!white to get 70% red red!10!white for 10% red and 90% white. This mixing can be done with any color, and 30% white or for example red!50!green, blue!50!yellow or green!60!black. A dierent type of color mixing is supported, which allows to take 100% of each component. For rgb,2:red,1;green,1 will add 1/2 part red and 1/2 part green and we reproexample, duced the example from above. Using the denominator 1 instead of 2 leads to rgb,1:red,1;green,1 which uses 1 part red and 1 part green. Many programs allow to select pieces between rgb,255:red,231;green,84;blue,121 0, . . . , 255, so a denominator of 255 is useful. Consequently, uses 231/255 red, 84/255 green and 121/255. This corresponds to the standard RGB color (231, 84, 121). Other examples are rgb,255:red,32;green,127;blue,43, rgb,255:red,178;green,127;blue,43, rgb,255:red,169;green,178;blue,43. It is also possible to use RGB values, the HSV color model, the CMY (or CMYK) models, or the HTML color syntax directly. However, this requires some more programming. I suppose this is the fastest (and probably the most uncomfortable) method to use colors. For example,\definecolor{color1}{rgb}{1,1,0} \tikz \fill[color1] (0,0) rectangle (1em,0.6em);

creates the color with 60%

yellow and 10%

creates the color with 208/255 pieces red, 178/255 pieces green and 43 pieces blue, specied in standard HTML notation. Please refer to the xcolor manual [3] for more details and color models. The xcolor package provides even more methods to combine colors, among them the prex - (minus) which changes the color into its complementary color ( -black, -white, -red) or color wheel calculations. Please refer to the xcolor manual [3]. /tikz/color={ a color } /tikz/draw={ stroke color } /tikz/fill={ ll color } These keys are (generally) used to set colors. Use color to set the color for both drawing and lling. Instead of color={ color name } you can simply write color name . The draw and fill keys only set colors for stroking and lling, respectively.

Since these keys belong to Tik Z, the complete documentation can be found in the Tik Z manual [5, Section Specifying a Color]. Color Spaces Since pgfplots relies on xcolor, all mechanisms of xcolor to dene color spaces apply here as well. One of the most useful approaches is global color space conversion: if you want a document which contains only colors in the cmyk color spaces, you can say\usepackage[cmyk]{xcolor} \usepackage{pgfplots}

in order to convert all colors of the entire document (including all shaded) to cmyk. The same can be achieved by means of the xcolor statement \selectcolormodel.\selectcolormodel{cmyk}

4.7.6

Color Maps(initially hot)

/pgfplots/colormap name={ color map name }

Changes the current color map to the already dened map named color map name . The predened color map is hot The denition can be found in the documentation for colormap/hot. This, and further color maps, are described below. Colormaps can be used, for example, in scatter plots (see Section 4.5.10). You can use colormap to create new color maps (see below). /pgfplots/colormap={ name }{ color specication } Denes a new colormap named name according to color specication and activates it using colormap name={ name }. The color specication is a sequence of positions and associated colors where linear interpolation is applied in-between. The syntax is very similar as the one used for pgf shadings described in [5, VIII Shadings]: it is a semicolonseparated series of color type ( oset )=( color value ); :% possibility 1: like PGF shadings: rgb(0cm)=(1,0,0); rgb(1cm)=(0,1,0); rgb255(2cm)=(0,0,255); gray(3cm)=(0.3); color(4cm)=(green)

If the distance between successive colors is the same, the oset can be omitted. The ; separators are not necessary either:% (simplified) possibility 2: skip ; and length arguments: rgb=(1,0,0) rgb=(0,1,0) rgb255=(0,0,255) gray=(0.3) color=(green)

It is also possible to provide non-uniform distances between the dierent colors if all single positions can be projected onto a uniform grid. pgfplots will perform this interpolation automatically:33 Up to now, plot marks always have a stroke color (some also have a ll color). This restriction may be lifted in upcoming versions.

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% non uniform spacing example: the mesh width is provided as first % part of the specification. \pgfplotsset{colormap={violetnew} {[1cm] rgb255(0cm)=(25,25,122) color(1cm)=(white) rgb255(5cm)=(238,140,238)}}

In this last example, the mesh width has been provided explicitly and pgfplots interpolates the missing grid points on its own. It is an error if the provided positions are no multiple of the mesh width. The \pgfplotsset employs the public user interface to create a new color map named violetnew. The single colors can be separated by semicolons ;. The (optional) length describes how much of the bar is occupied by the interval, it is interpreted relative to the complete length. If the length argument is missing, it is taken to be the last specied length plus the last length dierence (the rst color defaults to 1cm in this case). Colormap Input Format Each entry in color specication has the form color model ( length )=( arguments ). Here, the length argument is optional as discussed above. The entries can be separated by semicolons ; or by white spaces. The leftmost entry must have length =0pt. As discussed, all entries will be placed on a uniform grid, i.e. the distance between adjacent length arguments has to be the same (see the previous paragraph for automatic generation of intermediate points). The complete length of a color map is irrelevant: it will be mapped linearly to an internal range anyway (for ecient interpolation). The only requirement is that the left end must be at 0. Available choices for color model are rgb which expects arguments of the form ( red , green , blue ) where each component is in the interval [0, 1], rgb255 which is similar to rgb except that each component is expected in the interval [0,255], gray in which case arguments is a single number in the interval [0, 1], color in which case arguments contains a predened (named) color like red or a color expression like red!50, cmyk which expects arguments of the form ( cyan , magenta , yellow , black ) where each component is in the interval [0, 1], cmyk255 which is the same as cmyk but expects components in the interval [0, 255], cmy which expects arguments of the form ( cyan , magenta , yellow ) where each component is in the interval [0, 1], hsb which expects arguments of the form ( hue , saturation , brightness ) where each component is in the interval [0, 1], Hsb which is the same as hsb except that hue is accepted in the interval [0, 360] (degree), HTML which is similar to rgb255 except that each component is expected to be a hex number between 00 and FF, wave which expects a single wave length as numeric argument in the range [363, 814]. 3,000% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.7. MARKERS, LINESTYLES, (BACKGROUND-) COLORS AND COLORMAPS The Colorspace of a Colormap

167

Attention: this section is essentially superuos if you have congured the xcolor package to override color spaces globally (for example by means of \usepackage[cmyk]{xcolor} before loading pgfplots), see the end of this subsection. Even though a colormap accepts lots of color spaces on input (in fact, it accepts most or all that xcolor provides), the output color of a colorspace has strict limitations. The output colorspace is the one in which pgfplots interpolates between two other colors. To this end, it transforms input colors to the output color space. The output colorspace is also referred to as the colorspace of a colormap. There are three supported color spaces for a colormap: the GRAY, RGB, and CMYK color spaces. Each access into a colormap requires linear interpolation which is performed in its color space. Color spaces make a dierence: colors in dierent color spaces may be represented dierently, depending on the output device. Many printers use CMYK for color printing, so providing CMYK colors might improve the printing quality on a color printer. The RGB color space is often used for display devices. The predened colormaps in pgfplots all use RGB. Whenever a new colormap is created, pgfplots determines an associated color space. Then, each color in this specic colormap will be represented in its associated color space (converting colors automatically if necessary). Furthermore, every access into the colormap will be performed in its associated color space and every returned mapped color will be represented with respect to this color space. Furthermore, every shading generated by shader=interp will be represented with respect to the colormaps associated color space. The color space is chosen as follows: in case colormap default colorspace=auto (the initial conguration), the color space depends on the rst encountered color in color specication . For rgb or gray or color, the associated color space will be RGB (as it was in all earlier versions of pgfplots). For cmyk, the associated color space will be CMYK. If colormap default colorspace is either gray, rgb or cmyk, this specic color space is used and every color is converted automatically. /pgfplots/colormap default colorspace=auto|gray|rgb|cmyk (initially auto) Allows to set the color space of every newly created colormap. The choices are explained in the previous paragraph. It is (not yet) possible to change the color space of an existing colormap; re-create it if conversion is required. The macro \pgfplotscolormapgetcolorspace{ name } denes \pgfplotsretval to contain the color space of an existing colormap name, if you are in doubt. Note that this option has no eect if you told xcolor to override the color space globally. More precisely, the use of\usepackage[cmyk]{xcolor}

or, alternatively,\selectcolormodel{cmyk}

will cause all colors to be converted to cmyk, and pgfplots honors this conguration. Consequently, both these statements cause all colors to be interpolated in the desired color space, and all output colors will use this colorspace. This is typically exactly what you need. Predened Colormaps Available color maps are shown below. /pgfplots/colormap/hot A style which installs the colormap\pgfplotsset{ colormap={hot}{color(0cm)=(blue); color(1cm)=(yellow); color(2cm)=(orange); color(3cm)=(red)} }

(style, no value)

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This is the precongured color map. /pgfplots/colormap/hot2 A style which is equivalent to

Note that this particular choice ships directly with pgfplots, you do not need to load the colormaps library for this value. This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/jet A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={jet}{rgb255(0cm)=(0,0,128) rgb255(1cm)=(0,0,255) rgb255(3cm)=(0,255,255) rgb255(5cm)=(255,255,0) rgb255(7cm)=(255,0,0) rgb255(8cm)=(128,0,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/blackwhite A style which is equivalent to\pgfplotsset{ colormap={blackwhite}{gray(0cm)=(0); gray(1cm)=(1)} }

Remark: The style bluered (re-)denes the color map and activates it. TEX will be slightly faster if you call \pgfplotsset{colormap/bluered} in the preamble (to create the color map once) and use colormap name=bluered whenever you need it. This remark holds for every color map style which follows. But you can simply ignore this remark. /pgfplots/colormap/cool A style which is equivalent to\pgfplotsset{ colormap={cool}{rgb255(0cm)=(255,255,255); rgb255(1cm)=(0,128,255); rgb255(2cm)=(255,0,255)} }

/pgfplots/colormap/violet A style which is equivalent to

CHAPTER 4. THE REFERENCE

\pgfplotscolormaptoshadingspec{ colormap name }{ right end size }{ \macro }

A command which converts a colormap into a pgf shadings color specication. It can be used in commands like \pgfdeclare*shading (see the pgf manual [5] for details). The rst argument is the name of a (dened) colormap, the second the rightmost dimension of the specication. The result will be stored in \macro .

% convert hot -> \result \pgfplotscolormaptoshadingspec{hot}{8cm}\result % define and use a shading in pgf: \def\tempb{\pgfdeclarehorizontalshading{tempshading}{1cm}}% % where \result is inserted as last argument: \expandafter\tempb\expandafter{\result}% \pgfuseshading{tempshading}%

The usage of the result \macro is a little bit lowlevel. Attention: pgf shadings are always represented with respect to the RGB color space. Consequently, even CMYK colormap name s will result in an RGB shading specication when using this method34 . Note that there more available choices in the colormaps library which needs to be loaded by means of \usepgfplotslibrary{colormaps}.

4.7.7

Cycle Lists Options Controlling Line Styles

/pgfplots/cycle list={ list } /pgfplots/cycle list name={ \macro }

Allows to specify a list of plot specications which will be used for each \addplot command without explicit plot specication. Thus, the currently active cycle list will be used if you write either \addplot+[ keys ] ...; or if you dont use square brackets as in \addplot[ explicit plot specication ] ...;. The list element with index i will be chosen where i is the index of the current \addplot command (see also the cycle list shift key which allows to use i + n instead). This indexing does also include plot commands which dont use the cycle list. There are several possibilities to change the currently active cycle list: 1. Use one of the predened lists35 , color (from top to bottom)

34 In case pgf should someday support CMYK shadings and you still see this remark, you can add the macro denition \def\pgfplotscolormaptoshadingspectorgb{0} to your preamble. 35 In an early version, these lists were called \coloredplotspeclist and \blackwhiteplotspeclist which appeared to be unnecessarily long, so they have been renamed. The old names are still accepted, however.

The mark list always employs the current color, but it doesnt dene one (the \addplot+ statement explicitly sets the current color to blue). The mark list is especially useful in conjunction with cycle multi list which allows to combine it with other lists (for example linestyles or a list of colors). mark list* A list containing only markers. In contrast to mark list, all these markers are lled. They are dened as (from top to bottom) 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

auto The cycle list name=auto always denotes the most recently used cycle list activated by cycle list or cycle list name. The denitions of all predened cycle lists follow (see the end of this paragraph for a syntax description).

This is not the complete truth: the actual implementation of mark list allows to customize the fill value: /pgfplots/mark list fill={ color } Allows to customize the ll color for the mark list and mark list*. For example, if you have black as color, the alternative choice mark list fill=.!50!white will produce much better results. (initially .!80!black)

(This example list requires \usetikzlibrary{plotmarks}). The input format is described below in more detail. 3. The last method is to combine 1. and 2.: Dene named cycle lists in the preamble and use them with cycle list name: \pgfplotscreateplotcyclelist{ name }{ list }\pgfplotscreateplotcyclelist{mylist}{% {blue,mark=*}, {red,mark=square}, {dashed,mark=o}, {loosely dotted,mark=+}, {brown!60!black,mark options={fill=brown!40},mark=otimes*}} ... \begin{axis}[cycle list name=mylist] ... \end{axis}

The format of list : The argument list is usually a comma separated list of lists of style keys like colors, line styles, marker types and marker styles. This comma list of comma lists structure requires to encapsulate the inner list using curly braces:\pgfplotscreateplotcyclelist{mylist}{% {blue,mark=*}, {red,mark=square}, {dashed,mark=o}, {loosely dotted,mark=+}, {brown!60!black,mark options={fill=brown!40},mark=otimes*}}

In this case, the last entry also needs a terminating \\, but one can omit braces around the single entries. Remark: It is possible to call \pgfplotsset{cycle list={ a list }} or cycle list name between plots. Such a setting remains eective until the end of the current TEX group (that means curly braces). Every \addplot command queries the cycle list using the plot index; it doesnt hurt if cycle lists have changed in the meantime. /pgfplots/cycle multi list= list 1 \nextlist list 2 \nextlist Allows to supply more than one cycle list in a way such that each one contributes to the plot style. This is probably best explained using an example: 0 1 2 3 4 5 6 7 8 9 10 11

The provided cycle multi list consists of three lists. The style for a single plot is made up using elements of each of the three lists: the rst plot has style red,solid,mark=*, the second has

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177

red,solid,mark=x, the third has red,solid,mark=o. The fourth plot restarts the third list and uses the next one of list 2: it has red,dotted,mark options={solid},mark=* and so on. The last list will always be advanced for a new plot. The list before the last (in our case the second list) will be advanced after the last one has been reset. In other words: cycle multi list allows a composition of dierent cycle list in a lexicographical way36 . The argument for cycle multi list is a sequence of arguments as they would have been provided for cycle list, separated by \nextlist. In addition to providing a new cycle list, the list i elements can also denote cycle list name values (including the special auto cycle list which is the most recently assigned cycle list or cycle list name). The nal \nextlist is optional. The list in our example above could have been written as\begin{axis}[ cycle multi list={ red\\blue\\\nextlist solid\\dotted,mark options={solid}\\\nextlist mark=*\\mark=x\\mark=o\\ }]

CHAPTER 4. THE REFERENCE Using SubLists The list i entry can also contain just the rst n elements of an already known cycle list name using the syntax [ number of] cycle list name . For example [2 of]mark list will use the rst 2 elements of mark list: Cycle 2 marks between successive plots, then colors 0 1 2 3 4 5 6 7 8 9 10 11

/pgfplots/cycle list shift={ integer }

(initially empty)

Allows to shift the index into the cycle list. If integer is n, the list element i + n will be taken instead of the ith one. Remember that i is the index of the current \addplot command (starting with 0). Since a cycle list is queried immediately when \addplot (or \addplot+) is called, you can adjust the cycle list shift for selected plots:\pgfplotsset{cycle list shift=3} \addplot .... \pgfplotsset{cycle list shift=-1} \addplot ....

Special case: If the result is negative, i + n < 0, the list index (i + n) will be taken. For example, cycle list shift=-10 and i < 10 will result in list index 10 i. Note that you can use reverse legend to reverse legends, so this feature is probably never needed.

4.8. PROVIDING COLOR DATA - POINT META

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4.7.8

Axis Background(initially empty)

/pgfplots/axis background

This is a style to congure the appearance of the axis as such. It can be dened and/or changed using the axis background/.style={ options } method. A background path will be generated with options , which may contain ll colors or shadings.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Providing Color Data - Point Meta

pgfplots provides features which modify plots depending on a special coordinate, the point meta data. For example, scatter plots may vary marker colors, size or appearance depending on this special data. Surface and mesh plots are another example: here, the color of a surface patch (or mesh part) depends on point meta. The meta data of a node is not the position (which is given as (x, y ) or (x, y, z )). It is some information about that node; you could say: it is a specic property of the node. This is commonly called meta data. In pgfplots, every node has its coordinate and its meta data. Thus, twodimensional plots have three values: x, y , and the point meta data. Threedimensional plots have four values for each coordinate: x, y , z , and the point meta. In many cases, point meta is interpreted to be color data. To be more precise: it is interpreted to be scalar color data which is mapped into the colormap (more about this approach in the next paragraphs). However, point meta can be anything. Often, it is a single number as in the case of color data. That number is mapped linearly to the interval [0, 1000] such that 0 corresponds to the smallest encountered value and 1000 corresponds to the largest encountered scalar value. The mapped value is available as \pgfplotspointmetatransformed. This special value allows to dene some property of the plot: it can be the color (together with colormap). It can also be the line width in a mesh plot (more precisely: the line width could be dened to depend on the transformed meta data). The value can also be used to dene mark size. However, point meta data does not necessarily need to be a number. It can be a text label

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(any text that you like). This is used by nodes near coords, for example. It could also contain a tuple like RGB color information (which is not commonly used, however). Thus, point meta is really some abstract information about individual coordinates. Note that there is only one point meta per point. See the key visualization depends on if you need more than one meta data value per coordinate. The common idea idea is to tell pgfplots how to get the meta data. It is not necessary to provide data explicitly in many cases, the data which is used to color surface patches or marker colors is the plots y or z coordinate. The method used to tell pgfplots where to nd point meta data is the point meta key. The most common use-case of point meta is color information: if the point meta data is in the interval [mmin , mmax ], the point meta coordinate m = mmin will get the lowest color provided by the color map while m = mmax will get the highest color provided by the color map. As already mentioned, this is accomplished using \pgfplotspointmetatransformed [0, 1000] (per convention). Any coordinate between the smallest and largest values will be mapped linearly: for example, the mean m = 1/2(mmax + mmin ) will get the middle color of the color map (it will have \pgfplotspointmetatransformed = 500). This is why point meta is sometimes called color data in this manual.

The point meta key tells pgfplots where to get the special point meta data. Please note that point meta and scatter src is actually the same scatter src is an alias for point meta. Thus, the summary provided for scatter src on page 98 covers the same topics. However, the main reference for point meta is here. none The initial choice none disables point meta data, resulting in no computational work. Any other choice will activate the computation of upper and lower ranges for point meta data, i.e. the computation of [mmin , mmax ]. x The choice x uses the already available x coordinates as point meta data. This does always refer to the nal x coordinates after any user transformations, logarithms, stacked plot computations etc. have been applied. Consider using rawx if you need the unprocessed coordinate value here. y z The choices y and z are similar: they use the y or z coordinates respectively as point meta data. Consequently, these three choices do not need any extra data. As for x, there are math constants rawy and rawz which yield the unprocessed y and z value, respectively. f(x) This will use the last available coordinate, in other words: it is the same as y for two dimensional plots and z for three dimensional ones.

explicit This choice tells pgfplots to expect numerical point meta data which is provided explicitly in the coordinate input streams. This data will be transformed linearly into the current color map as it has been motivated above.

Thus, there are several methods to provide point meta (color data). The key for the choice explicit is that some data is provided explicitly although point meta doesnt know how. The data is expected to be of numerical type and is mapped linearly into the range [0, 1000] (maybe for use in the current color map). explicit symbolic The choice explicit symbolic is very similar to explicit in that it expects extra data by the coordinate input routines. However, explicit symbolic does not necessarily expect numerical data: you can provide any sort of symbols. One might provide a set of styles, one for each class in a scatter plot. This is realised using scatter/classes, see page 100. Input data is provided in the same fashion as mentioned above for the choice explicit. Currently, this choice can only be used for scatter plots.

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CHAPTER 4. THE REFERENCE expression This choice allows to compute point meta data using a mathematical expression. The expression may depend on x, y, z which yield the current x, y or z coordinate, respectively. The coordinates are completely processed (transformations, logs) as mentioned above for the choice x. Furthermore, the expression may depend on commands which are valid during \addplot like \plotnum or \coordindex (see Section 4.26 for details). Computations are performed using the oating point unit of pgf, and all supported arithmetical operations can be used. In essence, the expression may depend on everything which is known to all \addplot commands: the x, y and (if any) z coordinates. In addition, it may depend upon rawx, rawy or rawz. These three expressions yield the unprocessed x, y or z value as it has been found in the input stream (no logs, no user transformations)37 . If used together with plot table, you may also access other table columns (for example with \thisrow{ colname }). TeX code= code A rather low level choice which allows to provide TEX code to compute a numerical value. The code should dene the macro \pgfplotspointmeta. It is evaluated in a locally scoped environment (its local variables are freed afterwards). It may depend on the same values as described for expression above, especially on \thisrow{ colname } for table input. Note that the math parser will be congured to use the fpu at this time, so \pgfmathparse yields oats. Note that you need an extra pair of braces to provide this key, i.e. point meta={TeX code={ code }}. TeX code symbolic= code Just as TeX code, you can provide code which denes the macro \pgfplotspointmeta, but the result is not interpreted as a number. It is like the explicit symbolic choice. Note that you need an extra pair of braces to provide this key, i.e. point meta={TeX code symbolic={ code }}. symbolic= symbol A choice which accepts some arbitrary symbol which is used for every coordinate. As explicit symbolic and TeX code symbolic, this choice yields symbolic representations, i.e. it is kept asis without mapping the result. The dierence to explicit symbolic is that symbol is a common symbol for all points whereas explicit symbolic expects the input data stream (like a table) to provide individual symbols. The dierent to TeX code symbolic is marginal: symbolic is actually the same as point meta/TeX code symbolic={\def\pgfplotspointmeta{ symbol }}. A use-case for symbolic is mesh/color input=explicit mathparse, see the documentation therein. Note that you need an extra pair of braces to provide this key, i.e. point meta={symbolic={ symbol }}. As already mentioned, a main application of point meta data is to determine (marker/face/edge) colors using a linear map into the range [0, 1000] (maybe for use in the current color map). This map works as follows: it is a function : [mmin , mmax ] [0, 1000] m mmin 1000 such that (mmin ) = 0 and (mmax ) = 1000. The value 1000 is per convention the upper limit of all color maps. Now, if a coordinate (or edge/face) has the point meta data m, its color will be determined using (m): it is the color at (m) of the current color map. (m) = This transformation depends on the interval [mmin , mmax ] which, in turn, can be modied using the keys point meta rel, point meta min and point meta max described below. The untransformed point meta data is available in the macro \pgfplotspointmeta (only in the correct context, for example the scatter plot styles or the scatter/@pre marker code interface). This macro contains a low level oating point number (unless it is non-parsed string data). The transformed data will be available in the macro \pgfplotspointmetatransformed and is in xed point representation. It is expected to be in the range [0, 1000]. with

rare circumstances, it might be interesting to apply a math expression to another source of point meta (one of the other choices. To this end, the expression is checked after the other possible choices have already been evaluated. In other words, the statement point meta=explicit, point meta=meta*meta+3 will evaluate the expression with meta set to whatever data has been provided explicitly.

Sets point meta= point meta source , but only if point meta=none currently. This is used for scatter, mesh and surf with set point meta if empty=f(x). /pgfplots/point meta rel=axis wide|per plot (initially axis wide) As already explained in the documentation for point meta, one application for point meta data is to determine colors using the current color map and a linear map from point meta data into the current color map. The question is how this linear map is computed. The key point meta rel congures whether the interval of all point meta coordinates, [mmin , mmax ] is computed as maximum over all plots in the complete axis (the choice axis wide) or only for one particular plot (the choice per plot). Axis wide color mapping Per Plot color mapping

Note that a colorbar will still use the axis wide point meta limits. Consider the colorbar source key if you want the color data limits of a particular plot for your color bar. The point meta rel key congures how point meta maps to colors in the colormap. /pgfplots/point meta min={ number } /pgfplots/point meta max={ number } These keys allow to dene the range required for the linear map of point meta data into the range [0, 1000] (for example, for current maps) explicitly. This is necessary if the same mapping shall be used for more than one axis. Remarks about special cases:

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It is possible to provide limits partially; in this case, only the missing limit will be computed. If point meta data falls outside of these limits, the linear transformation is still well dened which is acceptable (unless the interval is of zero length). However, color data cant be outside of these limits, so color bars perform a truncation. This key can be provided for single plots as well as for the complete axis (or for both). If meta limits are provided for a single plot, these limits may also contribute to the axis wide meta interval.

/pgfplots/colormap access=map|direct

(initially map)

This key congures how point meta data is used to determine colors from a color map. The initial conguration map performs the linear mapping operation explained above. The choice direct does not perform any transformation; it takes the point meta as integer indices into the current color map. Consequently, there is no interpolation between colors in the color map, there will only be as many colors as the color map contains explicitly. Some more details: If there are m colors in the color map and the color data falls outside of [0, m 1], it will be pruned to either the rst or the last color. If color data is a real number, it will be truncated to the next smaller integer. This key does not work for shader=interp (note that this shader will always interpolate in the color map).

Attention: This feature is experimental and has never been used or tested so far. If you believe that it should receive more attention, let us know.

4.9

Axis Descriptions

Axis descriptions are labels for x and y axis, titles, legends and the like. Axis descriptions are drawn after the plot is nished and they are not subjected to clipping.

4.9.1

Placement of Axis Descriptions

This section describes how to modify the placement of titles, labels, legends and other axis descriptions. It may be skipped at rst reading. There are dierent methods to place axis descriptions. One of them is to provide coordinates relative to the axis rectangle such that (0,0) is the lower left corner and (1,1) is the upper right corner this is very useful for gure titles or legends. Coordinates of this type, i.e. without unit like (0,0) or (1.03,1), are called axis description cs (the cs stands for coordinate system). One other method is of primary interest for axis labels they should be placed near the tick labels, but it a way that they dont overlap or obscure tick labels. Furthermore, axis labels shall be placed such that they are automatically moved if the axis is rotated (or tick labels are moved to the right side of the gure). There is a special coordinate system to realize these two demands, the ticklabel cs. In the following, the two coordinate systems axis description cs and ticklabel cs are described in more detail. It should be noted that axis description cs is used automatically, so it might never be necessary to use it explicitly. Coordinate system axis description cs A coordinate system which is used to place axis descriptions. Whenever the option at={( x , y )} occurs in label style, legend style or any other axis description, ( x , y ) is interpreted to be a coordinate in axis description cs. The point (0, 0) is always the lower left corner of the tightest bounding box around the axes (without any descriptions or ticks) while the point (1, 1) is the upper right corner of this bounding box. In most cases, it is not necessary to explicitly write axis description cs as it is the default coordinate system for any axis description. An example for how coordinates are placed is shown below.

Axis descriptions are Tik Z nodes, that means all placement and detail options of [5] apply. The point on the nodes boundary which is actually shifted to the at coordinate needs to be provided with an anchor (cf [5, Nodes and Edges]):

CHAPTER 4. THE REFERENCE Standard anchors of nodes are north, east, south, west and mixed components like north east. Please refer to [5] for a complete documentation of anchors. Remarks: Each of the anchors described in Section 4.19 can be described by axis description cs as well. The axis description cs is independent of axis reversals or skewed axes. Only for the default conguration of boxed axes is it the same as rel axis cs, i.e. (0,0) is the same as the smallest axis coordinate and (1,1) is the largest one in case of standard boxed axes38 . Even for three dimensional axes, the axis description cs is still two-dimensional: it always refers to coordinates relative to the tightest bounding box around the axis (without any descriptions or ticks).

system system system system system system system

38 This was dierent in versions before 1.3: earlier versions did not have the distinction between axis description cs and rel axis cs.

4.9. AXIS DESCRIPTIONS Coordinate system ticklabel* cs

187

A set of special coordinate systems intended to place axis descriptions (or any other drawing operation) besides tick labels, in a way such that neither tick labels nor the axis as such are obscured. See also xlabel near ticks as one main application of ticklabel cs. The xticklabel cs (and its variants) always refer to one, uniquely identied axis: the one which is (or would be) annotated with tick labels. The ticklabel cs (without explicit x, y or z) can only be used in contexts where the axis character is known from context (for example, inside of xlabel style there, the ticklabel cs is equivalent to xticklabel cs). The starred variants xticklabel* cs and its friends do not take the size of any tick labels into account. Each of these coordinate systems allows to specify points on a straight line which is placed parallel to an axis containing tick labels, moved away just far enough to avoid overlaps with the tick labels: Positioning with xticklabel csyticklabel cs:1

The basic idea is to place coordinates on a straight line which is parallel to the axis containing tick labels but shifted such that the line does not cut through tick labels. Note that an axis description which has been placed with xticklabel cs or its friends is also useful for skewed axes or the axis x line variants it is often the same value for all these variants. In particular, it is useful for threedimensional axes, see below. Typically, xticklabel cs places nodes exactly at the position where the largest associated tick label is nished. While this is very useful, it might be undesired for example if one wants to move into the opposite direction (here, the special anchor near ticklabel opposite might be of interest). To this end, there are the starred variants, i.e. xticklabel* cs and its friends:

The preceding example places all the additional anchors precisely onto the axis on which tick labels are drawn. The starred version xticklabel* cs ignores the size of tick labels. Of course, it is relatively simple to get the same coordinates as in the two dimensional example above with axis description cs, except that ticklabel cs always respects the tick label sizes appropriately. However, ticklabel cs becomes far superior when it comes to three dimensional positioning: Positioning with ticklabel cs in 3D

The coordinate ticklabel cs:0 is associated with the lower axis limit while ticklabel cs:1 is near the upper axis limit. The value 0.5 is in the middle of the axis, any other values (including negative values or values beyond 1) are linearly interpolated inbetween. All coordinate systems like ticklabel cs also accepts a second (optional) argument: a shift away from the tick labels. The shift points to a vector which is orthogonal39 the associated axis, away from the tick labels. A shift of 0pt is directly at the edge of the tick labels in direction of the normal vector, positive values move the position away and negative closer to the tick labels. ticklabel cs and its optional shift

5 0 5 5 4 2 0 0 2 4 5xticklabel cs:1,0

xticklabel cs:1,15pt

39 Actually,

the outer normal has the impression of being orthogonal to its axis, which appears to be sucient.

Whenever the ticklabel cs is used, the anchor should be set to anchor=near ticklabel (see below). Whenever the starred version ticklabel* cs is used, both anchors anchor=near ticklabel and anchor=near ticklabel opposite are useful choices. There is one specialty: if you reverse an axis (with x dir=reverse), points provided by ticklabel cs will be unaected by the axis reversal. This is intented to provide consistent placement even for reversed axes. Use allow reversal of rel axis cs=false to disable this feature. Besides the mentioned positioning methods, there is also the predened node current axis. The anchors of current axis can also be used to place descriptions: At the time when axis descriptions are drawn, all anchors which refer to the axis origin (that means the real point (0, 0)) or any of the axis corners can be referenced using current axis. anchor name . Please see Section 4.19, Alignment, for further details.

4.9.2

Alignment of Axis Descriptions

This section describes how to modify the default alignment of axis descriptions. It can be skipped at rst reading. The two topics positioning and alignment always work together: positioning means to select an appropriate coordinate and alignment means to select an anchor inside of the description which will actually be moved to the desired position. Tik Z uses many anchors to provide alignment; most of them are named like north, north east etc. These names hold for any axis description as well (as axis descriptions are Tik Z nodes). Readers can learn details about this topic in the Tik Z manual [5] or some more advice in Section 4.19. When it comes to axis descriptions, pgfplots oers some specialized anchors and alignment methods which are described below. Anchor Anchor Anchor Anchor near near near near xticklabel yticklabel zticklabel ticklabel

These anchors can be used to align at the part of a node (for example, an axis description) which is nearest to the tick labels of a particular axis (or nearest to the position where tick labels would have been drawn if there were any). These anchors are used for axis labels, especially for three dimensional axes. Furthermore, they are used for every tick label. Maybe it is best to demonstrate it by example:

The motivation is to place nodes such that they are anchored next to the tick label, regardless of the nodes rotation or the position of ticks. The special anchor near ticklabel is only available for axis labels (as they have a uniquely identied axis, either x, y or z ). In more detail, the anchor is placed such that rst, the nodes center is on a line starting in the nodes at position going in direction of the inwards normal vector of the axis line which contains the tick labels and second, the node does not intrude the axis (but see also the key near ticklabel align and the details in the lengthy elaboration in the documentation for near xticklabel opposite below). This normal vector is the same which is used for the shift argument in ticklabel cs: it is orthogonal to the tick label axis. Furthermore, near ticklabel inverts the transformation matrix before it computes this intersection point. The near ticklabel anchor and its friends will be added temporarily to any shape used inside of an axis. This includes axis descriptions, but it is not limited to them: it applies to every Tik Z \node[anchor=near xticklabel] ... setting. Note that it is not necessary at all to have tick labels in an axis. The anchor will be placed such that it is near the axis on which tick labels would be drawn. In fact, every tick label uses anchor=near

CHAPTER 4. THE REFERENCE

These anchors are similar to near xticklabel and its variants, except that they align at the opposite direction. Mathematically speaking, the only dierence to near xticklabel and its variants is the sign in front of the normal vector. But it is probably best explained by means of an example. near ticklabel (opposite)

The gure is a boxed threedimensional axis with standard ranges. It has three manually placed nodes. The nodes are placed at (xticklabel cs:0.2), at (xticklabel* cs:0.6), and at (yticklabel cs:1), respectively. The at locations are visually emphasized using lled circles. Despite the dierent locations, we clearly see the eect of near xticklabel opposite: it causes the node to be aligned into the box rather than outside of the box. Note that this is the only essential dierence between the two nodes near xticklabel opposite and near xticklabel. The gure also shows the dierence between xticklabel cs and xticklabel* cs when we compare

4.9. AXIS DESCRIPTIONS

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the at locations. Take, for example, the two nodes on the x axis. The position at (xticklabel cs:0.2) is shifted by the green arrow. The length of this arrow is precisely the length of the largest x tick label. The position at (xticklabel* cs:0.6) is exactly on the axis; it ignores the size of any tick labels. Note that the direction of the green arrow is the outer normal vector in x direction (in our case, it is the vector sum of the z and y unit vectors with appropriate signs). The dierence between near xticklabel opposite and near xticklabel is that the direction of the green arrow (the outer normal) is ipped. The nodes also highlight how the anchoring works. This technique is almost the same for both anchor=near xticklabel and anchor=near xticklabel opposite. Let us discuss the technique for the node with text near yticklabel. The black circle is placed at (yticklabel cs:1). This position has been computed by starting at 100% of the y axis40 and moving along the green vector whose magnitude is the size of the bounding box of the largest y tick label. As soon as the at location is xed, the algorithm for near yticklabel starts. First, it computes the anchor inside of the node for which we do not penetrate the y axis. To this end, it checks the direction of the green vector. It came up with north west. Then, it considers the red line which starts at (name.north west) and has the same direction as the y axis. Note that the red line and the y axis are parallel. It also considers the blue line. This line points into the direction of the green line and is xed by the current nodes center. The precise intersection point of the red line and the blue line are the result of anchor=near yticklabel. The same applies for the other two nodes as well: the red line is always parallel to the axis under consideration and is anchored at the snaptonearestanchor of the node. The blue line is always parallel to the outer normal vector of the axis under consideration, and is anchored at the current nodes center. /pgfplots/near ticklabel align=inside|center|outside (initially center)

Allows to change the alignment algorithm of anchor=near ticklabel. In the default conguration, anchor=near ticklabel and its variants take the nodes center in order to derive the nal anchor. This corresponds to the target of the blue line in the illustration for near xticklabel opposite, see above. This key changes the nodes anchor which is used here. The choice center can move half of the nodes bounding box beyond the associated axis. The choice inside moves the complete nodes bounding box in a way such that it is not beyond the associated axis. The choice outside moves the entire nodes bounding box in a way that it is beyond the associated axis: near ticklabel align

0 .5 1 0 0outside.

0.2

0.4

0.5 0 .6 0.8inside.

1 0center.

40 In

our example, percentages and absolute values are accidentally the same.

The example is similar to the one above: it generates an empty axis with a default range. Then, it creates three nodes: one for choice center, one for choice inside, and one for choice outside. The node for center is placed at (yticklabel cs:0) (lower black circle). We see that its bounding box extends the size of the y axis. This is because its anchor C.center is used for the alignment. Both the node for inside and the node for outside are placed at (yticklabel cs:1) (upper black circle). Their only dierence is the choice for near ticklabel align. The node for inside does not extend the size of the y axis; it is placed within its boundaries because its internal anchor (I.north east) (blue) has automatically been used in order to align the node. The node for outside is completely outside of the extends for the y axis because its (blue) anchor (O.south west) has been chosen. Note that the red lines are always the same. They are the snaptonearest anchor such that the node is outside of the axis. Only the location of the blue anchors is aected by this key. Note that near ticklabel align always results in the same alignment, independent of the actual position of the node. This is because an anchor is independent of the at location of a node. In this context, the names inside and outside might be a bad choice: they stress the intended meaning if the node is chosen at the upper end of the axis. However, if you say at (yticklabel cs:0), near ticklabel align=inside, it will actually end up outside of the axis. This is because the inside anchor has been computed without considering where the node is. /tikz/sloped /tikz/sloped /tikz/sloped /tikz/sloped /tikz/sloped /tikz/sloped like like like like like like x y z x y z axis axis axis axis={ options } axis={ options } axis={ options } (no value) (no value) (no value)

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A key which replaces the rotational / scaling parts of the transformation matrix such that the node is sloped like the provided axis. For two dimensional plots, sloped like y axis is eectively the same as rotate=90. For a three dimensional axis, this will lead to a larger dierence:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Inside of axis labels, sloped is an alias for sloped like char automatically.

axis with the correct char chosen

Please note that rotated text might not look very good (neither on screen nor printed). It is possible to customize sloped like x axis by means of the following keys, which need to be provided as options (simply ignore the lengthy gray key prexes): /pgfplots/sloped/allow upside down=true|false (initially false) Use sloped like x axis=allow upside down to enable upside down labels. (initially empty)

/pgfplots/sloped/execute for upside down=code

Use sloped like x axis={execute for upside down=\tikzset{anchor=north}} or something like that to handle upside down text nodes in a customized way (this is used by the smithchart library). /pgfplots/sloped/reset nontranslations=true|false (initially true)

Use sloped like x axis={reset nontranslations=false} to append the transformations to the actual transformation matrix (instead of replacing it).

4.9.3

Labels

/pgfplots/xlabel={ text } /pgfplots/ylabel={ text } /pgfplots/zlabel={ text } These options set axis labels to text which is any TEX text. To include special characters, you can use curly braces: xlabel={, = characters}. This is necessary if characters like = or , need to be included literally. Use xlabel/.add={ prex }{ sux } to modify an already assigned label. Labels are Tik Z-nodes which are placed with% for x: \node [style=every axis label, style=every axis x label] % for y: \node [style=every axis label, style=every axis y label]

so their position and appearance can be customized. For example, a multiline xlabel can be congured using

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\begin{axis}[xlabel style={align=right,text width=3cm},xlabel=A quite long label with a line break] ... \end{axis}

Shifts labels in direction of the outer normal vector of the axis by an amount of dimension . The label shift sets all three label shifts to the same value. Attention: This does only work if \pgfplotsset{compat=1.3} (or newer) has been called (more precisely: if xlabel near ticks is active for the respective axis). /pgfplots/xlabel near ticks /pgfplots/ylabel near ticks /pgfplots/zlabel near ticks /pgfplots/compat=1.3 (no value) (no value) (no value)

These keys place axis labels (like xlabel) near the tick labels. If tick labels are small, labels will move closer to the axis. If tick labels are large, axis labels will move away from the axis. This is the default for every three dimensional plot, but it wont be used initially for twodimensional plots for backwards compatibility. Take a look at the denition of near ticklabel on page 190 for an example. The denition of these styles is\pgfplotsset{ /pgfplots/xlabel near ticks/.style={ /pgfplots/every axis x label/.style={ at={(ticklabel cs:0.5)},anchor=near ticklabel } }, /pgfplots/ylabel near ticks/.style={ /pgfplots/every axis y label/.style={ at={(ticklabel cs:0.5)},rotate=90,anchor=near ticklabel } } }

It is encouraged to write\pgfplotsset{compat=1.3} % or newer

in your preamble to install the styles document-wide it leads to the best output (it avoids unnecessary space). It is not activated initially for backwards compatibility with older versions which used xed distances from the tick labels. /pgfplots/xlabel absolute /pgfplots/ylabel absolute /pgfplots/zlabel absolute /pgfplots/compat=pre 1.3 (no value) (no value) (no value)

Installs placement styles for axis labels such that xlabel yields a description of absolute, xed distance to the axis. This is the initial conguration (for backwards compatibility with versions before 1.3). Use compat=1.3 to get the most recent, more exible conguration. Take a look at the denition of near ticklabel on page 190 for an example. These styles are dened by

The titles appearance and/or placement can be recongured with

This will place the title at 75% of the x-axis. The coordinate (0, 0) is the lower left corner and (1, 1) the upper right one (see axis description cs for details). Use title/.add={ prex }{ sux } to modify an already assigned title. /pgfplots/extra description/.code={ ... } Allows to insert commands after axis labels, titles and legends have been typeset. As all other axis descriptions, the code can use (0, 0) to access the lower left corner and (1, 1) to access the upper right one. It wont be clipped.

Legends can be generated in two ways: the rst is to use \addlegendentry or \legend inside of an axis. The other method is to use the key legend entries. \addlegendentry[ options ]{ name } Adds a single legend entry to the legend list. This will also enable legend drawing. 3 Case 1 Case 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

It does not matter where \addlegendentry commands are placed, only the sequence matters. You will need one \addlegendentry for every \addplot command (unless you prefer an empty legend). The optional options aect how the text is drawn; they apply only for this particular description text. For example, \addlegendentry[red]{Text} would yield a red legend text. Behind the scenes, the text is placed with \node[ options ] { name };, so options can be any Tik Z option which aects nodes. Using \addlegendentry disables the key legend entries. \addlegendentryexpanded[ options ]{ TEX text } A variant of \addlegendentry which provides a method to deal with macros inside of TEX text . Suppose TEX text contains some sort of parameter which varies for every plot. Moreover, you like to use a loop to generate the plots. Then, it is simpler to use \addlegendentryexpanded:

Note that this example wouldnt have worked with \addlegendentry{$x^\p$} because the macro \p is no longer dened when pgfplots attempts to draw the legend. The invocation \addlegendentryexpanded{$x^\p$} is equivalent to calling \addlegendentry{$x^2$} if \p expands to 2. The argument TEX text is expanded until nothing but un-expandable material remains (i.e. it uses the TEX primitive \edef). Occasionally, TEX text contains parts which should be expanded (like \p) and other parts which should be left unexpanded (for example \pgfmathprintnumber{\p}). Then, use \noexpand\pgfmathprintnumber{\p} or, equivalently \protect\pgfmathprintnumber{\p} to avoid expansion of the macro which follows the \protect immediately. \legend{ list } You can use \legend{ list } to assign a complete legend.\legend{$d=2$,$d=3$,$d=4$,$d=5$,$d=6$}

The argument of \legend is a list of entries, one for each plot. Two dierent delimiters are supported: 1. There are commaseparated lists like\legend{$d=2$,$d=3$,$d=4$,$d=5$,$d=6$}

These lists are processed using the pgf \foreach command and are quite powerful. The \foreach command supports a dotsnotation to denote ranges like \legend{1,2,...,5} or even \legend{$x^1$,$x^...$,$x^d$}. Attention with periods: to avoid confusion with the dots ... notation, you may need to encapsulate a legend entry containing periods by curly braces: \legend{{ML spcm.},{CW spcm.},{ML AC}} (or use the \\ delimiter, see below). 2. It is also possible to delimit the list by \\. In this case, the last element must be terminated by \\ as well:\legend{$a=1, b=2$\\,$a=2, b=3$\\$a=3, b=5$\\}

This syntax simplies the use of , inside of legend entries, but it does not support the dots notation. The short marker/line combination shown in legends is acquired from the style options argument of \addplot. Using \legend overwrites any other existing legend entries. /pgfplots/legend entries={ comma separated list }

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CHAPTER 4. THE REFERENCE This key can be used to assign legend entries just like the commands \addlegendentry and \legend. Again, the positioning is relative to the axis rectangle (unless units like cm or pt are specied explicitly). x x2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Please be careful with whitespaces in comma separated list : they will contribute to legend entries. Consider using % at the end of each line in multiline arguments (the end of line character is also a whitespace in TEX). Just as for \addlegendentry, it is possible to provide [ options ] to single descriptions. To do so, place the options in square brackets right before the text: x x2 x3% Preamble: \pgfplotsset{width=7cm,compat=1.9}

will draw it at the lower left corner of the axis while

means the upper right corner. The anchor option determines which point of the legend will be placed at (0, 0) or (1, 1). The legend is a Tik Z-matrix, so one can use any Tik Z option which aects nodes and matrices (see [5, section 13 and 14]). The matrix is created by something like\matrix[style=every axis legend] { draw plot specification 1 & \node{legend 1}\\ draw plot specification 2 & \node{legend 2}\\ ... };

They are actually just styles for commonly used alignment choices: the choice left is equivalent to legend style={cells={anchor=west}}; the second choice right is equivalent to legend style={cells={anchor=east}}, and center to legend style={cells={anchor=center}}. Using different values allows more control over cell alignment. /pgfplots/legend columns={ number } (default 1)

Congures where the small line specications will be drawn: left of the description, right of the description or not at all. (style, no value)

/pgfplots/every legend image post

A style which can be used to provide drawing options to every small legend image. These options apply after current plot style has been set, allowing users dierent line styles for legends than for plots.

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205

For example, suppose you have a line plot and you plot selected markers on top of it (in the same color). Then, you may want to draw just a single legend entry (which should contain both the line and the markers). The following example shows a solution: 1 Parabola% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example has two \addplot commands, one for the line and one for markers. Due to the forget plot option, the marker plot (the rst one) doesnt advance the cycle list. The axis has only one legend entry, and since legend image post style={mark=*} has been used, the legend has a plot mark as well. Due to the forget plot option, the marker plot will not get a separate legend label. /pgfplots/legend image post style={ key-value-list } An abbreviation for every legend image post/.append style={ key-value-list }. It appends options to the already existing style every legend image post. /pgfplots/legend image code/.code={ ... } Allows to replace the default images which are drawn inside of legends. When this key is evaluated, the current plot specication has already been activated (using \begin{scope}[current plot style])41 , so any drawing operations use the same styles as the \addplot command. The default is the style line legend. Technical note: At the time when legend images are drawn, the style every axis legend is in eect which have unwanted side-eects due to changed parameters (especially those concerning node placement, alignment, and shifting). It might be necessary to reset these parameters manually (pgfplots also attempts to reset the ll color). /pgfplots/line legend A style which sets legend image code (back) to its initial value. Its initial value is\pgfplotsset{ /pgfplots/line legend/.style={ legend image code/.code={ \draw[mark repeat=2,mark phase=2,##1] plot coordinates { (0cm,0cm) (0.3cm,0cm) (0.6cm,0cm) };% } } }

(style, no value)

The style line legend can also be used to apply a dierent legend style to one particular plot (see the documentation on area legend for an example). /pgfplots/empty legend A style which clears legend image code, thereby omitting the legend image.41 This

(style, no value)

was dierent in versions before 1.3. The new scope features allow plot styles to change legend image code.

(initially false) (initially false)

Allows to transpose the order in which the pairs (legend entry, plot style) are drawn. Consider a set of 3 experiments, each consisting of 2 parameters. We might want to draw them together as in the following example: A1 B1 C1 10 A2 B2 C2

\addplot {-1.2*x + 4}; \addplot {-1.2*x + 5};

Thus, legend columns denes the input columns, before the transposition (in other words, legend columns indicates the rows of the resulting legend). Transposing legends has only an eect if legend columns> 1. Note that reverse legend has higher precedence: it is applied rst.

4.9.6

A pgfplots oers a \label and \ref feature for L TEX to assemble a legend manually, for example as part of A the gure caption. These references work as usual L TEX references: a \label remembers where and what needs to be referenced and a \ref expands to proper text. In context of plots, a \label remembers the plot specication of one plot and a \ref expands to the small image which would also be used inside of legends.

The picture shows the estimations \ref{pgfplots:label1} which are subjected to noise. It appears the model \ref{pgfplots:label2} fits the data appropriately. Finally, \ref{pgfplots:label3} is only here to get three examples.

The picture shows the estimations which are subjected to noise. It appears the model appropriately. Finally, is only here to get three examples. \label{ label name } \label[ reference ]{ label name }

ts the data

A When used after \addplot, this command creates a L TEX label named label name 42 . If this label is cross-referenced with \ref{ label name } somewhere, the associated plot specication will be inserted.

Label3 =42 This

; Label2 =

Label3 = \ref{pgfplots:label3}; Label2 = \ref{pgfplots:label2}

A feature is only available in L TEX, sorry.

210

CHAPTER 4. THE REFERENCE The label is assembled using legend image code and the plot style of the last plot. Any pgfplots option is expanded until only Tik Z (or pgf) options remain; these options are used to get an independent label. More precisely, the small image generated by \ref{ label name } is\tikz[/pgfplots/every crossref picture] {...}

where the contents is determined by legend image code and the plot style. The second syntax, \label[ reference ]{ label name } allows to label particular pieces of an \addplot command. It is (currently) only interesting for scatter/classes: there, it allows to reference particular classes of the scatter plot. See page 100 for more details. Note that \label information, even the small Tik Z pictures here, can be combined with the external library for image externalization, see Section 7.1 for details (in particular, the external/mode key). In other words, references remain valid even if the dening axis has been externalized. \ref{ label name } Can be used to reference a labeled, single plot. See the example above. This will also work together with hyperref links and \pageref43 . /pgfplots/refstyle={ label name } Can be used to set the styles of a labeled, single plot. This allows to write\addplot[/pgfplots/refstyle={pgfplots:label2}]

somewhere. Please note that it may be easier to dene a style with .style. /pgfplots/every crossref picture A style which will be used by the cross-referencing feature for plots. The default is\pgfplotsset{every crossref picture/.style={baseline,yshift=0.3em}}

(style, no value)

/pgfplots/invoke before crossref tikzpicture={ TEX code } /pgfplots/invoke after crossref tikzpicture={ TEX code } Code which is invoked just before or just after every cross reference picture. This applies to legend images generated with \ref, legend to name and colorbar to name images. The initial conguration checks if the external library is in eect. If so, it modies the generated gure names by means of \tikzappendtofigurename{_crossref}.

4.9.7

Legends Outside Of an Axis

Occasionally, one has multiple adjacent plots, each with the same legend and just one legend suces. But where shall it be placed? And how? One solution is to use the overlay key to exclude the legend from bounding box computations, and place it absolutely such that it ts. Another is the legend to name feature: /pgfplots/legend to name={ name } (initially empty)

Enables a legend export mode: instead of drawing the legend, a selfcontained, independent set of drawing commands will be stored using the label name . The denition is done using \label{ name }, A just like any other L TEX label. The name can be referenced using \ref{ name }. Thus, typing \ref{ name } somewhere outside of the axis, maybe even outside of any picture, will cause the legend to be drawn.43 Older versions of pgfplots required the use of \protect\ref when used inside of captions or section headings. This is no longer necessary.

Note that only the rst plot has legend entries. Thus, its legend will be created as usual, and stored under the name named, but it wont be drawn. The stored legend can then be drawn with \ref{named} below the three plots. Since there is no picture in this context, a \tikz picture is created and a \matrix[/pgfplots/every axis legend] path is drawn inside of it, resulting in the legend as if it had been placed inside of the axis. The stored legend will contain the currently active values of legend- and plot style related options. This includes legend image code, every axis legend, and any plot style options (and some more). The algorithm works in the same way as for \label and \ref, i.e. it keeps any options with /tikz/ prex and expands those with /pgfplots/ prex. Note that the legend is drawn with every axis legend, even though the placement options might be chosen to t into an axis. You may want to adjust the style in the same axis in which the stored legend has been dened (the value will be copied and restored as well). About \ref{ name } to name) and draws it. The \ref{ name } command retrieves a stored legend (one dened by legend

212(x + 0)k ; (x + 1)k ; (x + 2)k ;

CHAPTER 4. THE REFERENCE

(x + 3)k

\ref{named}:

If you want the legend to be exported and drawn inside of the current axis, consider using extra description/.append code={\ref{ name }}. Note that \ref can be combined with the external library for image externalization. In other words, the legend will work even if the dening axis has been externalized, see Section 7.1 for details (in particular the external/mode key). Note furthermore that this .aux le related stu is (currently) only supported, if pgfplots is run by A means of L TEX, sorry. \pgfplotslegendfromname{ name } This command poses an equivalent alternative for \ref{ name }: it has essentially the same eect, but it does not create links when used with the hyperref package44 . /pgfplots/every legend to name picture (style, no value) A style which is installed when \ref is used outside of a picture: a new picture will be created with \tikz[/pgfplots/every legend to name picture]. Thus, you can redene this style to set alignment options (such as baseline). For example, the initialization\pgfplotsset{ legend style={matrix anchor=west,at={(0pt,0pt)}}, every legend to name picture/.style={baseline}, } ...

will cause the legend to be positioned such that its west anchor is at y=0pt. The baseline option will align this point of the legend with the text baseline (please refer to the documentation for baseline in Section 4.19 for details).

4.9.8

Legends with Customized Texts or Multiple Lines

\addlegendimage{ options } Adds a further legend image for legend creation. Each \addplot command appends its plot style options to a list, and \addlegendimage adds options to the very same list. Thus, the eect is as if you had provided \addplot[ options ], but \addlegendimage bypasses all the logic usually associated with a plot. In other words: except for the legend, the state of the axis remains as if the command would not have been issued. Not even the current plots index is advanced. x x2 x3 x 1 x 2 x 3% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example above has six plots, each with its legend entry. Furthermore, it has an \addlegendimage command and its separate legend entry. We see that \addlegendimage needs its own legend entry, but it is detached from the processing of plots as such. In our case, we chose empty legend as style for the separator.44 Since this manual uses colored links, the text in \ref would usually be blue. Using \pgfplotslegendfromname avoids link text colors in the legend (this has been applied to the manual styles here).

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213

Use \addlegendimage to provide custom styles into legends, for example to document custom \draw commands inside of an axis. You can call \label after \addlegendimage just as for a normal style. Occasionally, one may want multiple lines for legend entries. That is possible as well using a xed text width: 102

The example provides options for the single multiline element. Note that the initial conguration of legend style employs text depth=0.15em, which needs to be reset manually to text depth={}45 . There are two approaches with the same eect which are subject of the following example: 102 101 100 101 102 0 1 2 3 x x2 x3 Neg. Sign: x 1 x 2 x 3 4% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the legend entries are provided using the single key syntax. Note that the special options are provided as part of the legend entry, using square brackets right before the text as such. The comments indicate that you could also add the text width stu to legend style, in which case it would hold for every node. Note that legend texts are realized using \node[ options ] { text };, so anything which produces a valid Tik Z node is permitted (this includes minipage or tabular environments inside of text ).

4.9.9

Axis Lines

An extension by Pascal Wolkotte

By default the axis lines are drawn as a box, but it is possible to change the appearance of the x and y axis lines. /pgfplots/axis x line=box|top|middle|center|bottom|none /pgfplots/axis x line*=box|top|middle|center|bottom|none /pgfplots/axis y line=box|left|middle|center|right|none45 Perhaps

I can reset text depth automatically in the future.

CHAPTER 4. THE REFERENCE (initially box)

These keys allow to choose the locations of the axis lines. The last one, axis lines sets the same value for every axis. Ticks and tick labels are placed according to the chosen value as well. The choice bottom will draw the x line at y = ymin , middle will draw the x line at y = 0, and top will draw it at y = ymax . Finally, box is a combination of options top and bottom. The choice axis x line=none is an alias for hide x axis. The y - and z variants work in a similar way. The case center is a synonym for middle, both draw the line through the respective coordinate 0. If this coordinate is not part of the axis limit, the lower axis limit is chosen instead. The starred versions . . . line* only aect the axis lines, without correcting the positions of axis labels, tick lines or other keys which are (possibly) aected by a changed axis line. The non-starred versions are actually styles which set the starred key and some other keys which also aect the gure layout: In case axis x line=box, the style every boxed x axis will be installed immediately. In case axis x line=box, the style every non boxed x axis will be installed immediately. Furthermore, some of these choices will modify axis label positions.

if the matching y style has value axis y line=right and

if axis y line=right. Feel free to overwrite these styles if the default doesnt t your needs or taste. Again, these styles will not be used for axis line*. 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

In case middle, the style every inner axis x line allows to adjust the appearance. Note that three dimensional axes only support to use the same value for every axis, i.e. three dimensional axes support only the axis lines key (or, preferably for 3D axes, the axis lines* key check what looks best). See Section 4.11.4 for examples of three dimensional axis line variations.

CHAPTER 4. THE REFERENCE (no value) (no value) (no value)

A style key which can be redened to customize the appearance of inner axis lines. Inner axis lines are those drawn by the middle (or center) choice of axis x line, see above. This style aects only the line as such. y3 100% Preamble: \pgfplotsset{width=7cm,compat=1.9}

217 (no value)

(no value) (no value) (no value)

A style which will be installed as soon as axis x line (y) will be set to something dierent than box.

with similar values for the y-variant. Feel free to redene this style to your needs and taste. /pgfplots/separate axis lines={ true,false } (default true) Enables or disables separate path commands for every axis line. This option aects only the case if axis lines are drawn as a box. Both cases have their advantages and disadvantages, I fear there is no reasonable default (suggestions are welcome). The case separate axis lines=true allows to draw arrow heads on each single axis line, but it cant close edges very well in case of thick lines, unsatisfactory edges occur.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The case separate axis lines=false issues just one path for all axis lines. It draws a kind of rectangle, where some parts of the rectangle may be skipped over if they are not wanted. The advantage is that edges are closed properly. The disadvantage is that at most one arrow head is added to the path (and yes, only one drawing color is possible).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE

4.9.10

Two Ordinates (y axis) or Multiple Axes

In some applications, more than one y axis is used if the x range is the same. This section demonstrates how to create them. The idea in pgfplots is to draw two axes on top of each other, one with descriptions only on the left and the second with descriptions only on the right:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Thus, the two axes are drawn on top of each other one, which contains the x axis and the left y axis, and one which has only the right y axis. Since pgfplots does not really know what its doing here, user attention in the following possibly non-obvious aspects is required: 1. Scaling. You should set scale only axis because this forces equal dimensions for both axis, without respecting any labels. 2. Same x limits. You should set those limits explicitly. 3. You need to tell pgfplots that it should share the same graphics layers for both axes. In this case, pgfplots will draw plots of the rst axis and of the second axis onto the same layer. It will also draw background(s) into the background layer and descriptions into the foreground layer. Use the key \pgfplotsset{set layers} in front of the rst axis to prepare the complete picture for layered graphics. You may want to consider dierent legend styles. It is also possible to use only the axis, without any plots: 1,000 per thousand 20 Absolute 800 600 10 400 200 0 4 2 0 x 2 4 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.9. AXIS DESCRIPTIONS

219

4.9.11

Axis Discontinuities

An extension by Pascal Wolkotte

In case the range of either of the axis do not include the zero value, it is possible to visualize this with a discontinuity decoration on the corresponding axis line. /pgfplots/axis x discontinuity=crunch|parallel|none /pgfplots/axis y discontinuity=crunch|parallel|none /pgfplots/axis z discontinuity=crunch|parallel|none (initially none) (initially none) (initially none)

Insert a discontinuity decoration on the x (or y , respectively) axis. This is to visualize that the y axis does cross the x axis at its 0 value, because the minimum x axis value is positive or the maximum value is negative. The description applies to axis y discontinuity and axis z discontinuity as well, simply substitute x by y or z , respectively.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The options xtickmin, xtickmax and ytickmin, ytickmax allow to dene the axis tick limits, i.e. the axis values before respectively after no ticks will be placed. Everything outside of the axis tick limits will be not drawn. Their default values are equal to the axis limits.

/pgfplots/hide /pgfplots/hide /pgfplots/hide /pgfplots/hide

Allows to hide either a selected axis or all of them. No outer rectangle, no tick marks and no labels will be drawn. Only titles and legends will be processed as usual. Axis scaling and clipping (!) will be done as if you did not use hide axis. x2 cos(x)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

This can be used to embed a pgfplots path which needs an axis to a standard Tik Z picture. See also Section 4.27 for details how to synchronize the alignment between a pgfplots gure (which typically rescales its coordinates) to that of a standard tikzpicture. Note that pgfplots uses the input coordinates to determine the bounding box of the picture. In this case, the bounding box is slightly smaller than the shading. A cure would be to increase the bounding box manually. You may want to disable the clip path using the option clip=false.

4.9.12

Color Bars

pgfplots supports mesh, surface and scatter plots which can use color maps. While color maps can be chosen as described in Section 4.7.6, they can be visualized using color bars. /pgfplots/colorbar=true|false (initially false)

A color bar is only useful for plots with nonzero color data range, more precisely, for which minimum and maximum point meta data is available. Usually, this is the case for scatter, mesh or surf (or similar) plots, but you can also set point meta min and point meta max manually in order to draw a colorbar. Color bars are just normal axes which are placed right besides their parent axes. The only dierence is that they inherit several styles such as line width and fonts and they contain a bar shaded with the color map of the current axis. Color bars are drawn internally with\axis[every colorbar,colorbar shift,colorbar=false] \addplot graphics {}; \endaxis

where the placement, alignment, appearance and other options are done by the two styles every colorbar and colorbar shift. These styles and the possible placement and alignment options are described below. Remarks for special cases: Since there is always only one color bar per plot, this color bar uses the axis wide congurations of color map and color data. Consider using colorbar source to select color data limits of a particular \addplot command instead.

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If someone needs more than one color bar, the draw command above needs to be updated. See the key colorbar/draw/.code for this special case.

/pgfplots/colorbar right

(style, no value)

A style which redenes every colorbar and colorbar shift such that color bars are placed right of their parent axis. This is the initial conguration. 10 10 8 6 5 4 2 0 0 1 2 3

Attention: colorbar left re denes every colorbar. That means any user customization must take place after colorbar left (see also the documentation for colorbar right). /pgfplots/colorbar horizontal (style, no value)

A style which re-denes every colorbar and colorbar shift such that color bars are placed below their parent axis, with a horizontal bar.

CHAPTER 4. THE REFERENCE This style governs the placement, alignment and appearance of color bars. Any desired detail changes for color bars can be put into this style. Additionally, there is a style colorbar shift which is set after every colorbar. The latter style is intended to contain only shift transformations like xshift or yshift (making it easier to overwrite or deactivate them). While a color bar is drawn, the predened node parent axis can be used to align at the parent axis. Predened node parent axis A node for the parent axis of a color bar. It is only valid for color bars. Thus,\pgfplotsset{ colorbar style={ at={(parent axis.right of north east)}, anchor=north west, }, colorbar shift/.style={xshift=0.3cm} }

places the colorbar in a way that its top left (north west) corner is aligned right of the top right corner (right of north east) of its parent axis. Combining this with the colorbar shift is actually the same as the initial setting. Since color bars depend on some of its parents properties, these properties are available as values of the following keys: /pgfplots/point meta min /pgfplots/point meta max (no value) (no value)

The values of these keys contain the lower and upper bound of the color map, i.e. the lower and upper limit for the color bar. The value is \pgfkeysvalueof{/pgfplots/point meta min} inside of every colorbar. The value is usually determined using the axis wide point meta limits, i.e. they are computed as minimum and maximum value over all plots (unless the user provided limits manually). Consider the colorbar source key if youd like to select point meta limits of one specic \addplot command. /pgfplots/colorbar source={ true,false } (initially false)

Allows to select a specic \addplot command whose point meta limits are taken as upper and lower limit of a colorbars data range. This aects the tick descriptions of the colorbar. It needs to be provided as argument to \addplot, i.e. using\addplot[...,colorbar source] ... % or \addplot+[colorbar source] ...

or as key inside of a cycle list. Using colorbar source automatically implies point meta rel=per plot for that specic plot. If there are more than one \addplot commands with colorbar source, the last one is selected. /pgfplots/parent axis width /pgfplots/parent axis height (no value) (no value)

The values of these keys contain the size of the parent axis. They can be used as width and/or height arguments for every colorbar with \pgfkeysvalueof{/pgfplots/parent axis width}. These values are only valid inside of color bars. Besides these values, each color bar inherits a list of styles of its parent axis, namely every tick, every minor tick, every major tick, every axis grid, every minor grid,

4.9. AXIS DESCRIPTIONS

every major grid, every tick label.

227

This can be used to inherit line width and/or fonts. Customization: colorbar top 0.5 1 1.5 2 2.5 3% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Please take a look at the predened styles colorbar right, colorbar left and colorbar horizontal for more details about conguration possibilities for every colorbar. Remark: A color bar is just a normal axis. That means every colorbar can contain specications where to place tick labels, extra ticks, scalings and most other features of a normal axis as well (except nested color bars). /pgfplots/colorbar style={ key-value list } A shortcut for every colorbar/.append style={ key-value list }. It appends options to the colorbar style. /pgfplots/colorbar/width={ dimension } Sets the width of a color bar. (initially 0.5cm)

For horizontal color bars, this sets the height. /pgfplots/colorbar shift (style, no value)

This style is installed after every colorbar. It is intended to contain only shift transformations like xshift and/or yshift. The reason to provide two separate styles is to allow easier deactivation of shift transformations.\pgfplotsset{ colorbar shift/.style={xshift=1cm} }

Predened node current colorbar axis A predened node for the color bar of an axis. After \end{axis}, this node can be used to align further graphical elements at the color bar. Note that current axis refers to the axis as such while current colorbar axis refers to the color bar (which is an axis itself). /pgfplots/colorbar/draw/.code={ ... } This code key belongs to the low level interface of color bars. It is invoked whenever a color bar needs to be drawn. Usually, it wont be necessary to use or modify this key explicitly. When this key is invoked, the styles inherited from the parent axis are already set and the required variables (see the documentation of every colorbar) are initialized. This code key can be replaced if one needs more than one color bar (or other wrinkles). The initial conguration is\pgfplotsset{colorbar/draw/.code={% \axis[every colorbar,colorbar shift,colorbar=false] \addplot graphics {}; \endaxis } }

Please note that a color bar axis is nothing special as such it is just a normal axis with one plot graphics command and it is invoked with a special set of options. The only special thing is that a set of styles and some variables are inherited from its parent axis. /pgfplots/colorbar sampled={ optional options } A style which installs a discretely sampled color bar. (style, default surf,mark=none,shader=flat)

4.9. AXIS DESCRIPTIONS 1 1 0.5 0 0 0.5 1 6 4 2 0 2 4 6 1

The style uses \addplot3[ options ] to draw the colorbar, with domain set to the color range and the current value of the samples key to determine the number of samples. In other words: it uses plot expression and a surface plot to visualize the colorbar. Use colorbar style={samples=10} to change the number of samples. 1 1 0.5 0 0 0.5 1 6 4 2 0 2 4 6 1

The options can be used to change the \addplot3 options used for the colorbar visualization. For example, colorbar sampled={surf,shader=interp} will use Gouraud shading which has visually the same eect as the standard color bar. /pgfplots/colorbar sampled line={ optional options } (style, default scatter,only marks)

A style which draws a discrete colorbar. In contrast to colorbar sampled, it visualizes the colorbar using a line plot, not a surf plot.

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The initial conguration uses a scatter plot to visualize the colorbar, it can be changed by specifying options . Furthermore, the axis appearance is changed using axis y line*=left|right, depending on the position of the color bar (or axis x line*=bottom for colorbar horizontal). Consider the tick align=outside feature if you prefer tick lines outside of the colorbar instead of inside. /pgfplots/every colorbar sampled line It is initially set to help lines. (style, no value)

A style which is used by colorbar sampled line to change the color of the line without ticks.

4.9.13

Color Bars Outside Of an Axis

Occasionally, one has multiple adjacent plots, each with the same colormap and the same point meta min and point meta max values and wed like to show a single colorbar. pgfplots supports the colorbar to name feature which is similar to the related method for legends, legend to name: /pgfplots/colorbar to name={ name } (initially empty) Enables to detach a colorbar from its parent axis: instead of drawing the colorbar, a selfcontained, independent set of drawing commands will be stored using the label name . The label is dened using A \label{ name }, just as for any other L TEX label. The name can be referenced using \ref{ name }. Thus, typing \ref{ name } somewhere outside of the axis, maybe even outside of any picture, will cause the colorbar to be drawn.1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0 0.2 0.4 0 .6 0.8 1

The feature works in the same way as described for legend to name, please refer to its description on page 210 for the details. We only summarize the dierences here. \pgfplotscolorbarfromname{ name } This command poses an equivalent alternative for \ref{ name }: it has essentially the same eect, but it does not create links when used with the hyperref package. /pgfplots/every colorbar to name picture (style, no value)

A style which is installed when \ref is used outside of a picture: a new picture will be created with \tikz[/pgfplots/every colorbar to name picture]. See also the every legend to name picture style.

4.10

Scaling Options

There are a various options which control or change the scaling of an axis. Here, scaling typically means two aspects: rst, the unit vector size in each direction and second, the displayed limits in each direction. Both together control the size of the axis box. In addition, axis descriptions change the size. However, pgfplots scales only units and determines limits. It does not scale axis descriptions by default in order to keep consistent font sizes between the text and the gure. Often, one wishes to provide the target size only and let pgfplots do the rest. This is the default; it scales the axis to width and height. If you provide one of these options, the axis will be rescaled while keeping the aspect ratio. Occasionally, one wants to provide unit vectors explicitly to ensure that one unit takes a prescribed amount of space. This is possible by means of the x, y, and z keys. In such a case, the width and height options will be ignored (or only applied for the unspecied unit vectors). Another common approach is to enforce specic unit vector ratios: for example by specifying that each unit should take the same amount of space using axis equal. Here, pgfplots scales the lengths of all vectors uniformly, i.e. it applies the same scale to each vector. This is done by means of the scale mode conguration which is basically one of scale mode=stretch to fill or scale mode=scale uniformly: pgfplots tries to satisfy the prescribed width and height arguments by nding a common scaling factor. In addition, it attempts to enlarge the limits individually to t into the prescribed dimensions. In addition, you can use the option /pgfplots/scale to simply scale all nal units up by some prescribed factor. This does not change text labels. If needed, you can also supply /tikz/scale to an axis. This will scale the complete resulting image, including all text labels.

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4.10.1

Common Scaling Options

(initially empty)

All common options mentioned in the previous paragraphs are described here. /pgfplots/width={ dimen } Sets the width of the nal picture to { dimen }. Any non-empty dimension like width=5cm sets the desired target width. Any TEX unit is accepted (like 200pt or 5in). An empty value width={} means use default width or rescale proportionally to height. In this case, pgfplots uses the value of \axisdefaultwidth as target quantity. However, if the height key has been set, pgfplots will rescale the \axisdefaultwidth in a way which keeps the ratio between \axisdefaultwidth and \axisdefaultheight. This allows to specify just one of width and height and keep aspect ratios. Consequently, if you specify just width=5cm but leave the default height={}, the scaling will respect the initial aspect ratio. The scaling aects the unit vectors for x, y , and z . It does not change the size of text labels or axis descriptions. 5 0 5% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Please note that pgfplots only estimates the size needed for axis- and tick labels. The estimate assumes a xed amount of space for anything which is outside of the axis box. This has the eect that the nal images may be slightly larger or slightly smaller than the prescribed dimensions. However, the xed amount is always the same; it is set to 45pt. That means that multiple pictures with the same target dimensions will have the same size for their axis boxes even if the size for descriptions varies. It is also possible to scale the axis box to the prescribed width/height. In that case, the total width will be larger due to the axis descriptions. However, the axis box lls the desired dimensions exactly. 5% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note: changing width and/or height changes only the unit vector sizes. In particular, it does not change the font size for any axis description, nor does it change the default spacing between adjacent tick labels. It is best-practice to use width/height for small changes, i.e. changes for which the font size should remain the same. Consider using one of the styles normalsize, small, footnotesize, or tiny which are described in Section 4.10.2 on page 243, and then change to your desired dimensions if you need a dierent quality of scaling. \axisdefaultwidth This macro denes the default width. It is preset to 240pt.

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This default width denes the aspect ratio which will be used whenever just one of width or height is specied: the aspect ratio is the ratio between \axisdefaultwidth and \axisdefaultheight. You can change it using\def\axisdefaultwidth{10cm}

/pgfplots/height={ dimen }

(initially empty)

Works in the same way as width except that an empty value height={} defaults to use either \axisdefaultheight or scale proportionally if just width has been changed. \axisdefaultheight This macro denes the default height. It is preset to 207pt. See \axisdefaultwidth. /pgfplots/scale only axis=true|false (initially false)

If scale only axis is enabled, width and height apply only to the axis rectangle. Consequently, the resulting gure is larger that width and height (because of any axis descriptions). However, the axis box has exactly the prescribed target dimensions. If scale only axis=false (the default), pgfplots will try to produce the desired width including labels, titles and ticks.

Allows to assign zero, one, two, or three of the target unit vectors. In this context, a unit vector is a twodimensional vector which denes the projection onto the canvas: every logical plot coordinate (x, y ) is drawn at the canvas position x exx e + y yx . exy eyy

Note that if you change the unit vector for just one direction, the other vector(s) will be chosen by pgfplots and scaled in order to ll the prescribed width and height as best as pgfplots can (but see remarks for threedimensional plots at the end of this key). Height is deduced from height option 6% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The second syntax, x={( x , y )} sets ex = ( x , y )T explicitly47 . The corresponding keys for y and z work in a similar way. This allows to dene skewed or rotated axes.47 Please note that you need extra curly braces around the vector. Otherwise, the comma will be interpreted as separator for the next key-value pair.

Setting x and/or y for logarithmic axis will set the dimension used for 1 e 2.71828 (or whatever has been set as log basis x). Please note that it is not possible to specify x as argument to tikzpicture. The option\begin{tikzpicture}[x=1.5cm] \begin{axis} ... \end{axis} \end{tikzpicture}

does not have any eect because an axis rescales its coordinates (see the width option). Note that providing unit vectors explicitly usually causes pgfplots to ignore any other scaling options. In other words: if you say y=0.1cm, pgfplots will use (0cm, 0.1cm) as y projection vector. However, if you add scale mode=scale uniformly, you allow pgfplots to change the lengths of your vectors. Of course, it will keep their relative directions and relative sizes. In this case, pgfplots will try to determine a good common scaling factor and it will try to change the axis limits in order to ll the prescribed width and height (see the documentation for scale mode for details).

5 5 In the example above, pgfplots decided that it should only rescale units at the expensive of the width constraint. Changes to font sizes: labels in a simple way. see also Section 4.10.2 if you want to change font sizes or the density of tick

Explicit units for 3D axes: As of version 1.5, it is also possible to supply unit vectors to threedimensional axes. In this case, the following extra assumptions need to be satised: 1. If you want to control three-dimensional units, you need to provide all of x, y, and z keys. For twodimensional axes, it is also supported to supply just one of x or y. 2. Any provided three-dimensional unit vectors are assumed to form a righthanded coordinate system. In other words: take your right hand, let the thumb point into the x direction, the index nger in y direction and the middle nger in z direction. If that is impossible, the pgfplots output will be wrong. The reason for this assumption is that pgfplots needs to compute the view direction out of the provided units (see below). Consider using x dir=reverse or its variants in case you want to reverse directions. 3. For three-dimensional axes, pgfplots computes a view direction out of the provided unit vectors. The view direction is required to allow the z buffer feature (i.e. to decide about depths)48 . This feature is used to for the \addplot3 graphics feature, compare the examples in Section 4.3.8 on page 63. Limitations: Unfortunately, skewed axes are not available for bar plots. (initially normal) (initially normal) (initially normal)

Allows to choose between linear (=normal) or logarithmic axis scaling or logplots for each x, y, z combination. Logarithmic plots use the current setting of log basis x and its variants to determine the basis (default is e).

(initially normal) (initially normal) (initially normal)

Allows to reverse axis directions such that values are given in decreasing order. This key is documented in all detail on page 267.provides a debug option called view dir={ x }{ y }{ z } to override the view direction, should that ever be

48 pgfplots

interesting.

4.10. SCALING OPTIONS /pgfplots/axis equal={ true,false }

237 (initially false)

Each unit vector is set to the same length while the axis dimensions stay constant. Afterwards, the size ratios for each unit in x and y will be the same. Axis limits will be enlarged to compensate for the scaling eect.

The arguments rx , ry , and rz are ratios for x, y and z vectors, respectively. For twodimensional axes, only rx and ry are considered; they are provided relative to the y axis. In other words: the x unit vector will be rx / ry times longer than the y unit vector. For three-dimensional axes, all three arguments can be provided; they are interpreted relative to the z unit vector. Thus, a three dimensional axis with unit vector ratio=1 2 4 will have an x unit which is 1/4 the length of the z unit, and a y unit which is 2/4 the length of the z unit. Trailing values of 1 can be omitted, i.e. unit vector ratio=2 1 is the same as unit vector ratio=2; and unit vector ratio=3 2 1 is the same as unit vector ratio=3 2. An empty value unit vector ratio={} disables unit vector rescaling. Note that an active unit vector ratio will implicitly set scale mode=scale uniformly49 . /pgfplots/unit vector ratio*={ rx ry rz } /pgfplots/unit rescale keep size=true|false|unless limits declared limits declared) (initially unless

In the default conguration, pgfplots maintains the original axis dimensions even though unit vector ratio involves dierent scalings. It does so by enlarging the limits.49 This has been introduced in version 1.6. For older versions, the axis equal feature produced wrong results for three dimensional axes.

The example above has the same plot, with three dierent unit ratios. The rst has no limitations (it is the default conguration). The second uses the same length for each unit vector and enlarges the limits in order to maintain the same dimensions. The third example has an x unit which is 1/4 the length of a z unit, and an y unit which is 1/2 the length of a z unit. pgfplots does its best to respect the involved scaling options (the prescribed width and height, the unit vector ratio, and any specied axis limits). In the case above, it enlarged the horizontal limits and kept the z limit as-is. See scale mode and its documentation for details about the involved algorithm and its parameters. The unit rescale keep size=false key, or, equivalently, unit vector ratio*=..., does not enlarge limits:

The key unit rescale keep size also aects scale mode=scale uniformly (which is closely related to axis equal). Here is the reference of the value of unit rescale keep size: the value true means that pgfplots will enlarge limits in order to keep the size. It will try to respect user provided limits, but if the user provided all limits, it will override the user-provided limits and will rescale them. Thus, true gives higher priority to the axis size than to user-provided limits. The choice false will never rescale axis limits. The choice unless limits declared is a mixture: it will enlarge limits unless the user provided them. If the user provides all limits explicitly, this choice is the same as false. /pgfplots/x post scale={ scale } /pgfplots/y post scale={ scale } /pgfplots/z post scale={ scale } /pgfplots/scale={ scale } (initially (initially (initially (initially empty) empty) empty) empty)

Lets pgfplots compute the axis scaling based on width, height, view, plot box ratio, axis equal or explicit unit vectors with x, y, z and rescales the resulting vector(s) according to scale . The scale key sets all three keys to the same uniform scale value. This is eectively the same as if you rescale the complete axis (without changing sizes of descriptions). The other keys allow individually rescaled axes.

Scaling Descriptions: Predened Styles

It is reasonable to change font sizes, marker sizes etc. together with the overall plot size: Large plots should also have larger fonts and small plots should have small fonts and a smaller distance between ticks. /tikz/font=\normalfont|\small|\tiny|. . . /pgfplots/max space between ticks={ integer } /pgfplots/try min ticks={ integer } /tikz/mark size={ integer } These keys should be adjusted to the gures dimensions. Use\pgfplotsset{tick label style={font=\footnotesize}, label style={font=\small}, legend style={font=\small} }

to provide dierent fonts for dierent descriptions. The keys max space between ticks and try min ticks are described on page 287 and congure the approximate distance and number of successive tick labels (in pt). Please omit the pt sux here. There are a couple of predened scaling styles which set some of these options: /pgfplots/normalsize Re-initialises the standard scaling options of pgfplots. A normalsize gure 40 Leg (style, no value)

As for small, it can be convenient to set footnotesize and set width afterwards. You will need compat=1.3 or newer for this to work. /pgfplots/tiny (style, no value) Redenes several keys such that the axis is very small. Most descriptions will have \tiny as fontsize.A tiny gure10 The y axis 8 6 4 2 0 0 1 2 3 4 5 Leg % Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE As for small, it can be convenient to use tiny,width=4.5cm to adjust the width. You will need compat=1.3 or newer for this to work.

4.10.3

Scaling Strategies

The content of this section is quite involved and its knowledge is typically unnecessary because by default, pgfplots controls the involved stu automatically. You may want to skip this section. /pgfplots/scale mode=auto|none|stretch to fill|scale uniformly (initially auto)

Species how to choose the (individual) unit vector scaling factors, their length ratios, and perhaps the axis limits in order to ll the prescribed width and height. The scale mode implementation expects some initial set of unit vectors. This initial set of unit vectors is determined as follows: for standard twodimensional axes, it is simply the unit cube ex = (1pt, 0pt)T , ey = (0pt, 1pt)T , ez = 0. For threedimensional axes, it is the outcome of the two keys view and plot box ratio. If you provided units explicitly by means of one of x, y, or z, this value is the initial unit vector. In addition, it expects initial axis limits (i.e. values of xmin, xmax, etc.). The initial axis limits are those limits which have been deduced from your data or which have been provided explicitly. Furthermore, the initial axis limits already include changes of the enlargelimits key. Given the initial set of unit vectors and the initial axis limits, the scale mode implementation is a kind of postprocessor which creates modied unit vectors and modied axis limits in order to satisfy all specied constraints. These constraints are width, height, and unit vector ratio. The initial choice auto tells pgfplots to take full control over this key. It chooses one of the other possible choices depending on the actual context. The choice auto evaluates to scale uniformly if unit vector ratio is set. Otherwise it evaluates to stretch to fill.

The choice none does not apply any rescaling at all. Use this if prescribed lengths of x, y (and perhaps z) should be used. In other words: it ignores width and height. In this case, you may want to set x post scale and its variants to rescale units manually. See also disabledatascaling. The choice stretch to fill takes the initial unit vectors and rescales the unit vectors with two separate scales: one which results in the proper width and one which results in the proper height. As a consequence, the unit vectors are modied and distorted such that the nal image ts into the prescribed dimensions. This is usually what one expects unless one provides unit directions explicitly. This mode does not change axis limits. Note that if one of the unit vectors has been provided explicitly, pgfplots will not change it. It will only change the remaining axis limits. This mode contradicts axis equal or unit vector ratio. The choice scale uniformly takes the initial unit vectors and applies only one scaling factor to all units. In this case, there is just one common scaling factor for both width and height. Naturally, this will result in unsatisfactory results because either the nal width or the nal height will not be met. Therefore, this choice will adjust axis limits to get the desired dimensions. Thus, the unit vectors have exactly the same size relations and angles as they had before the scaling; only their magnitude is changed uniformly. In addition, axis limits may be changed (with individual scaling factors for each axis limit). Note that if unit vectors have been provided explicitly, pgfplots can still rescale it with this choice it will keep the relative directions and size ratios. The choice scale uniformly tries its best to modify the degrees of freedom in a useful way. The precise meaning of useful is the scale uniformly strategy key. /pgfplots/scale uniformly strategy=auto|units only|change vertical limits| change horizontal limits (initially auto) The scale uniformly method requires to determine one common scaling factor which rescales every axis unit. In addition, it allows one scaling factor for each axis limit, i.e. up to three. The constraints for this search are that we want to satisfy the width/height constraint, have as few rescaling as possible and that we do not want to reduce limits (as this could possibly hide data points). The choice auto chooses one of the other possibilities automatically. Depending on whether we have two dimensions or three dimensions, it compares the available methods and chooses the one which does not reduce limits and which involves the fewest rescaling (i.e. it may compare the outcome of

4.10. SCALING OPTIONS

247

the other strategies). This is the default. If you keep the choice auto, you do not have to worry about the remaining choices. Note that manually provided axis limits will not be modied. The choice units only will not enlarge axis limits. It will only rescale the units. To this end, it chooses the scaling factor such that the smaller target dimension is lled as desired. In other words: if width < height, it will scale to satisfy the width constraint. The height constraint will be ignored. The case > will be done the other way round. The choice units only typically results in a square axis as it takes the initial set of unit vectors (which are typically the unit box) and scales them with a common scaling factor. Consequently, you can choose units only if you want a boxed axis. You can still change axis limits manually, however. The choice change vertical limits chooses a common scaling factor for the unit vectors on order to satisfy the width (!) constraint. This common scaling factor is similar to units only but units only can also decide to satisfy the height constraint whereas change vertical limits will scale unit vectors to satisfy width. In order to satisfy the height constraint, change vertical limits modies just the vertical limits. For twodimensional axes, this is ymin and ymax. For threedimensional axes, this is zmin and zmax. Clearly, there is a chance that it will decrease the displayed range in this case, parts of the image will be clipped away. This method assumes that the vertical axis has not been rotated (i.e. that eyx = 0 or ezx = 0, respectively). It refuses to work and falls back to units only for rotates axes. Choose change vertical limits if you want the image (i.e. the actual content) as wide as possible. You can modify width and height to improve its outcome. Note that manually specied axis limits will not be changed, see below for details. The choice change horizontal limits attempts a similar approach, but for the horizontal limits: it determines one suitable scaling factor which is applied to all unit vectors and modies horizontal axis limits to satisfy the remaining constraints. For twodimensional axes, this is quite simple because we typically have exy = 0 (i.e. the x unit vector has vanishing y component) and eyx = 0 such that pgfplots can change axis limits easily. If a twodimensional axis has an x unit with exy = 0, the method is not applicable and falls back to units only. For threedimensional axes, it assumes that the z vector is not rotated, i.e. ezy = 0 and tries to change limits for both x and y . This choice is much more involved because here, x and y components are coupled. Consequently, the common unit scaling factor and the two involved axis limit compensation factors for x and y are tightly coupled as well. pgfplots solves a system of nonlinear equations iteratively to arrive at a suitable solution for all three scalings. Use this method if change vertical limits would clip away parts of the image (because it reduced the displayed range) and you do not want to change width and height. The choice change horizontal limits will typically result in more empty space in the resulting gure. But it will not clip away content. Manually specied axis limits will not be changed, see below for details. Manually provided axis limits: Any manually provided arguments for xmin and its variants are considered to be immutable; pgfplots will not change them. If you assign xmin, pgfplots will only change xmax and viceversa. If you assign both xmin and xmax, pgfplots will not change x limits at all. Note that if you assign both xmin and xmax, pgfplots will simply skip the scaling and will give up on the constraints. It will not try to compensate the lack of scaling opportunities by changing y limits, for example. This has the positive eect that assigning limits does not change the complete appearance of your axis. The allowed set of changes to axis limits can be congured with the following key. Interaction with enlargelimits: Note that enlargelimits and scale mode are independent of another: the outcome of enlargelimits is used as initial axis limits and these limits may be changed by scale mode (even if you said enlargelimits=false). See the documentation of enlargelimits for details on this interaction. /pgfplots/unit rescale keep size=true|false|unless limits declared (initially unless limits declared) In the default conguration unless limits declared, unit rescaling may cause changes to the axis limits in order to keep the gures size intact. However, only those limits which have not been declared manually are subject to rescaling: if you say xmin=1, only xmax and the limits for y and z are free to change. Setting unit rescale keep size=false will disable the modication of axis limits altogether, i.e. axis limits will not be rescaled to compensate scalings on unit vectors.

248

CHAPTER 4. THE REFERENCE Setting unit rescale keep size=true will always rescale limits, even if they have been declared manually. This key mainly aects scale mode=scale uniformly. This, in turn, is used for axis equal and \addplot3 graphics. See also the addition documentation for this key and related examples on page 239. The scale uniformly choice is implicitly used for axis equal and for the \addplot3 graphics feature, see the documentation in Section 4.3.8 on page 63 for its examples. Note that the common case is that the initial unit vectors form the unit cube (i.e. those before scaling, see above). In this case, scale uniformly is the same as axis equal.

4.11

3D Axis Conguration

This section described keys which are used to congure the appearance of three dimensional gures. Some of them apply for twodimensional plots as special case as well, and they will also be discussed in the respective sections of this manual.

4.11.1

View Conguration(initially {25}{30})

/pgfplots/view={ azimuth }{ elevation }

Changes both view angles of a 3D axis. The azimuth (rst argument) is the horizontal angle which is rotated around the z axis. For a 3D plot, the z axis always points to the top. The elevation (second argument) is the vertical rotation around the (rotated) x axis. Positive elevation values indicate a view from above, negative a view from below. All values are measured in degree. View along the positive y axis 5% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The view is computed as follows. The view is dened by two rotations: the rst rotation uses the azimuth angle to rotate around the z axis. Afterwards, the view is rotated elevation degrees around the rotated x axis (more precisely, it is rotated elevation degrees). The resulting transformed xz plane is the viewport, i.e. the view direction is always the transformed positive y axis. The view argument is compatible with the argument of the Matlab () view command, i.e. you can use [h,v] = view in matlab and pack the resulting arguments into pgfplots50 . If you work with gnuplot, you can convert the view arguments as follows: the gnuplot command set view v,h is equivalent to view={h}{90-v}. For example, the default gnuplot conguration set view 60,60 is equivalent to view={60}{30} in pgfplots. The view is (currently) always an orthogonal projection, no perspective is possible, yet. You can, however, specify projection unit vectors for x, y, and z explicitly to get a skewed threedimensional axis. /pgfplots/view/az={ azimuth } /pgfplots/view/h={ azimuth } (initially 25)

Changes only the azimuth view angle, i.e. the horizontal (rst) view angle which is rotated around the z axis.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/view/el={ elevation } /pgfplots/view/v={ elevation }

Changes only the vertical elevation, i.e. the second argument to view. Positive values view from above, negative values from below.

4.11.2

Styles Used Only For 3D Axes

(style, no value)

/pgfplots/every 3d description

This style allows to change the appearance of descriptions for three dimensional axes. Naturally, a three dimensional axis will display axis labels for x and y dierently than a two dimensional axis (for example, the y axis label wont be rotated by 90 degrees). The every 3d description style installs the necessary display options for three dimensional axis descriptions. The initial value is:

As the name suggests, every 3d description can only be used to set styles for axis labels, tick labels and titles. It has not been designed to reset other styles, you will need to change these options either for each axis separately or by means of user dened styles. The reason for this limitation is: other options can (and, in many cases, needs to) be set before the axis is processed. However, the decision whether we have a two dimensional or a three dimensional axis has to be postponed until the processing is more or less complete so only some remaining keys can be set. /pgfplots/every 3d view { h }{ v } A style which can be used for ne-tuning of the output for specic views. This style will be installed right after every 3d description, but before other axis description related keys are set (in other words: it has higher precedence than every 3d description, but lower precedence than keys provided to the axis directly). One example is precongured for view={0}{90} (from top):\pgfplotsset{ /pgfplots/every 3d view {0}{90}/.style={ xlabel near ticks, ylabel near ticks, axis on top=true } }

(style, no value)

4.11.3

Appearance Of The 3D Box

y stretch z stretch } (initially 1 1 1)

/pgfplots/plot box ratio={ x stretch

Allows to customize the aspect ratio between the three dierent axes in a three dimensional plot. Note that this key is dierent from the related unit vector ratio: the plot box is only useful for three dimensional axes, and it will usually distort the unit vector ratios. If you want equal unit ratios, consider using unit vector ratio. The plot box ratio is applied before any rotations and stretchtoll routines have been invoked. Thus, the initial setting51 1 1 1 makes all axes equally long before the stretchtoll routine is applied.51 Note

that you can also use the syntax {1}{1}{1} instead of space-separation.

This key applies only to three dimensional axes. After the scaling, the axes will be stretched to ll the width and height for this plot. Thus, the eects of plot box ratio might be undone by this stretching for particular views. /pgfplots/3d box=background|complete|complete* (initially background)

Allows to congure the appearance of boxed three dimensional axes. Type only 3d box (without value) as alias for 3d box=complete. The choice background is the initial setting, it does not draw axis lines (and grid lines) which are in the foreground. 3d box=background% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Before any foreground parts are actually processed, the style every 3d box foreground will be installed. This allows to change the appearance of foreground axis components like tick style or axis line style separately from the background components. Note that 3d box=complete is only available for boxed axes, i.e. together with axis lines=box. It is an error to use a dierent combination.

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4.11.4

Axis Line Variants

Three dimensional axes also benet from the axis lines=box or axis lines=center styles discussed in Section 4.9.9. The choice axis lines=box is standard, it draws a box (probably aected by the 3d box=complete key). The choice axis lines=center draws all three axes such that they pass through the origin. It might be necessary to combine this key with axis on top as there is no depth information.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The remaining choices axis lines*=left and axis lines*=right select dierent sets of axes in a way such that tick labels and axis label wont disturb the plots content. The * suppresses the use of special styles which are mainly adequate for two-dimensional axes, see the documentation of axis lines. Such a set of axes is always on the boundary of the two-dimensional projection. The choice axis lines*=left chooses a set of axes which are on the left (or bottom, respectively) whereas the choice axis lines*=right chooses a set of axes which are on the right (or top, respectively):% Preamble: \pgfplotsset{width=7cm,compat=1.9}

It is not possible to mix dierent styles like axis x line=center,axis z line=top.

4.12

Error Bars

An error bar is used to indicate the reliability of a data point. Typically, a data point is just (x, y ). The reliability would be indicated by additional values, i.e. by means of an error bound x which characterizes the dierence between the coordinate x provided in the plot data and the precise value x (which is unknown). The reliability can be indicated for both x and y independently (although y might be the typical candidate). Error bounds can be expressed as absolute errors, i.e. of the form |x x | x,

|y y |

4.12. ERROR BARS

255

where x and y are the (unknown) precise values and x and y are the actual values of the plot. However, they can also be provided relative to the input values, i.e. of the form |x x | |x |x,

|y y | |y |

y.

A relative error of 10% would result in an error value of 0.1 (relative to the precise quantity y ). Clearly, relative errors are only useful if the precise value if not zero, i.e. x , y = 0. pgfplots allows to provide the error values for each coordinate independently. Thus, it may nd some value x and/or y . Depending on the conguration, it interprets the encountered value as absolute or relative error. The error value can be the same for every coordinate, for example if you know that each y coordinate has a xed error of 10%. The error value can also be dierent for every coordinate in which it is said to be explicitly provided. In fact, pgfplots also features asymmetric error values, i.e. the lower bound on the error can be dierent from the upper bound. Thus, a twodimensional data point (x, y ) can have up to four distinct error values which have to be provided by the enduser. Thus, the enduser has to provide all needed error values and a conguration to express if these values are to be interpreted as relative or absolute error and if the values are to be expected explicitly for every data point or if they are xed.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example has two keys: y dir=plus congures pgfplots to activate error bars for y coordinates, but only upper bounds. The key y explicit tells pgfplots to expect absolute values in the input data stream. In our case above, the input data stream is an \addplot coordinates which uses the special errorvaluesyntax +- ( x , y ), see the Section 4.12.1 for details. It is allowed if the input data contains more error values than needed: our example above has error values for both x and y and it also contains lower bounds (since +- denes upper- and lower bounds simultaneously). Consequently, the remaining values can be visualized as well:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

256 /pgfplots/error bars/z dir=none|plus|minus|both

CHAPTER 4. THE REFERENCE (initially none)

The initial conguration none draws no error bars at all in the provided direction. The conguration plus draws only upper bounds in the direction of interest. The conguration minus draws only lower bounds in the direction of interest. The conguration both draws upper and lower bounds in the direction of interest. In every case, the actual error value and its character (absolute or relative) is to be determined by other options (see below). If, for some reason, the error value is missing, the error bar is omitted.

Congures the error bar algorithm to draw x-error bars at any input coordinate for which user-specied errors are available. Each error is interpreted as relative error, that means error marks are placed at x(1 value (x)) (works as for error bars/x fixed relative).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

where (1, 2) (0.4, 0.2) is the rst coordinate, (2, 4) (1, 0) the second and so forth. The point (3, 5) has no error coordinate. The syntax +- denes symmetric error values, i.e. both upper and lower bound receive the same value. Alternatively, one can use one of -= and += to dene asymmetric values:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

If multiple items (like multiple +=) for one coordinate are specied, the last one takes precedence. Keep in mind that these error values are only displayed as error bars if x dir and y dir are set appropriately. The input type \addplot coordinates also allows point meta=explicit, i.e. values of the form\addplot coordinates {(0,0) [4]};

This can be combined with error values. However, the point meta value in square brackets needs to be the last item:\addplot coordinates {(0,0) +- (0.1,0.2) [4]};

These keys dene input sources for error bars with explicit error values. The x error method provides an input column name (or alias), the x error index method provides input column indices and x error expr works just as table/x expr: it allows arbitrary mathematical expressions which may depend on any number of table columns using \thisrow{ col name }.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE

These keys dene input sources for error bars with asymmetric error values, i.e. dierent values for upper and lower bounds. They are to be used in the same way as x error. In fact, x error is just a style which sets both x error plus and x error minus to the same value.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Number Formatting Options

pgfplots typesets tick labels rounded to given precision and in congurable number formats. The command to do so is \pgfmathprintnumber; it uses the current set of number formatting options. In addition, pgfplots might prepare tick numbers before they are handed over to \pgfmathprintnumber. The options related to number printing as such are described in all detail in the manual for PgfplotsTable, which comes with pgfplots. This section contains the reference for everything which is specic to an axis, and only a brief survey over the number formatting options as such.

4.13.1

Frequently Used Number Printing Settings

This section provides a brief survey about the most frequently used aspects of number formatting in pgfplots. 1. pgfplots computes common tick scaling factors like 102 and produces only integers as tick labels. In order to get numbers like 0.001 as tick labels instead of 1 with a separate label 103 , you can use scaled ticks=false in your axis. See the description of scaled ticks for details.

2. In order to customize the way numbers are rounded and/or displayed, use something like xticklabel style={/pgf/number format/.cd,fixed,precision=5}. Here is a short list of possibilities: 123.46 12,345.68 12,345.6789\pgfmathprintnumber{123.456789}

\pgfmathprintnumber [1000 sep={\,},fixed,precision=6]{1000000.123456}

1 000 000.123 456

Each of these keys requires the prex /pgf/number format/ when used inside of a pgfplots style (try /pgf/number format/.cd, number formatting keys to use the same prex for many number formatting keys ). The number formatting uses \pgfmathprintnumber, a pgf command to typeset numbers. A full reference of all supported options is shipped with pgfplots: it is documented in the reference manual for PgfplotsTable, Section Number Formatting Options. The same reference can be found in the documentation for pgf. Note that the number printer knows nothing about pgfplots. In particular, it is not responsible for logs and their representation. 3. For a logarithmic axis, one may want to modify the number formatting style for the exponent only. In this case, redene the style log plot exponent style (its documentation contains a couple of examples). 4. In order to get fixed point tick labels on a logarithmic axis, you can use log ticks with fixed point (see below).

4.13.2

PGFPlots-specic Number Formatting

This section contains netuning options to change number formatting aspects but only things which are specic to pgfplots like peculiarities of tick labels on logarithmic axes. Consider browsing Section 4.13.1 rst to see if you need this section. \pgfmathprintnumber{ x } Generates pretty-printed output for the (real) number x . The input number x is parsed using \pgfmathfloatparsenumber which allows arbitrary precision. Numbers are typeset in math mode using the current set of number printing options, see below. Optional arguments can also be provided using \pgfmathprintnumber[ options ]{ x }. Please refer to the manual of PgfplotsTable (shipped with this package) for details about options related to number-printing.

262 /pgfplots/log ticks with fixed point

CHAPTER 4. THE REFERENCE (style, no value)

Recongures pgfplots to display tick labels of logarithmic axes using xed point numbers instead of the exponential style.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.13. NUMBER FORMATTING OPTIONS

263

Allows to congure the number format of log plot exponents. This style is installed just before log number format basis will be invoked. Please note that this style will be installed within the default code for log number format code. ex e2x 105.0 f (x) 101.7 100.0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

This key is set by the default styles for extra ticks. /pgfplots/log number format code/.code={ ... }

4.14. SPECIFYING THE PLOTTED RANGE

265

Provides TEX-code to generate log plot tick labels. Argument #1 is the (natural) logarithm of the tick position. The default implementation invokes log base 10 number format code after it changed the log basis to 10. It also checks the other log plot options. This key will have a dierent meaning when the log basis has been chosen explicitly, see the log basis x key. /pgfplots/log base 10 number format code/.code={ ... } Allows to change the overall appearance of base 10 log plot tick labels. The default implementation invokes log number format basis={10}{#1}. Use log plot exponent style if you only want to change number formatting options for the exponent. /pgfplots/log number format basis/.code={ ... } Typesets a logarithmic tick. The rst supplied argument is the log basis, the second the exponent. The initial conguration is\pgfplotsset{ /pgfplots/log number format basis/.code 2 args={$#1^{\pgfmathprintnumber{#2}}$} }

Use log plot exponent style if you only want to change number formatting options for the exponent.

4.144.14.1

Specifying the Plotted Range

Conguration of Limits Ranges

/pgfplots/xmin={ coord } /pgfplots/ymin={ coord } /pgfplots/zmin={ coord } /pgfplots/xmax={ coord } /pgfplots/ymax={ coord } /pgfplots/zmax={ coord } /pgfplots/min={ coord } /pgfplots/max={ coord } These options allow to dene the axis limits, i.e. the lower left and the upper right corner. Everything outside of the axis limits will be clipped away. Each of these keys is optional, and missing limits will be determined automatically from input data. Here, the min and max keys set limits for x, y and z to the same coord . If x-limits have been specied explicitly and y -limits are computed automatically, the automatic computation of y -limits will only considers points which fall into the specied x-range (and viceversa). The same holds true if, for example, only xmin has been provided explicitly: in that case, xmax will be updated only for points for which x xmin holds. This feature can be disabled using clip limits=false. Axis limits can be increased automatically using the enlargelimits option. Auto Limits% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that even if you provide ymax=10, data points with y > 10 will still be visualized producing a line which leaves the plotted range. See also the restrict x to domain and restrict x to domain* keys they allow to discard or clip input coordinates which are outside of some domain, respectively. During the visualization phase, i.e. during \end{axis}, these keys will be set to the nal axis limits. You can access the values by means of \pgfkeysvalueof{/pgfplots/xmin}, for example: Axis limits are [6 : 6] [2.5 : 27.5]% Preamble: \pgfplotsset{width=7cm,compat=1.9}

This access is possible inside of any axis description (like xlabel, title, legend entries etc.) or any annotation (i.e. inside of \node, \draw or \path and coordinates in (axis cs: x , y )), but not inside of \addplot (limits may not be complete at this stage). /pgfplots/xmode=normal|linear|log (initially normal)

267 (initially normal) (initially normal)

Allows to choose between linear (=normal) or logarithmic axis scaling or logplots for each x, y, z combination. Logarithmic plots use the current setting of log basis x and its variants to determine the basis (default is e).

Note that colorbars wont be reversed automatically, you will have to reverse the sequence of color bars manually in case this is required as in the preceding example. /pgfplots/clip limits=true|false (initially true)

Congures what to do if some, but not all axis limits have been specied explicitly. In case clip limits=true, the automatic limit computation will only consider points which do not contradict the explicitly set limits. This option has nothing to do with path clipping, it only aects how the axis limits are computed.

4.14. SPECIFYING THE PLOTTED RANGE

The choice rel={ value } is the same as true,value={ value }, i.e. it activates relative enlargement for both upper and lower limit. The value upper enlarges only the upper axis limit while lower enlarges only the lower axis limit. In this case, the amount added to the respective limit can be specied using the value={ val } key. It can be combined with any of the other possible values. For example, \pgfplotsset{enlarge x limits={value=0.2,upper}} will enlarge (only) the upper axis limit by 20% of the axis range. Another example is \pgfplotsset{enlarge x limits={value=0.2,auto}} which changes the default threshold of the auto value to 20%.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

While value uses relative thresholds, abs value accepts absolute values: it adds an absolute value to the selected axis. The choice abs={ value } is the same as true,abs value={ value }, i.e. it adds an absolute value to both upper and lower limit:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Technically, the use of absolute dimensions is a little bit dierent. For example, it allows to enlarge by more than width which is impossible for all other choices. pgfplots will try to fulll both the provided width/height and the absolute axis enlargements. If it fails to do so, it will give up on width/height constraints and print a warning message to your log le. See also the key enlargelimits respects figure size. Attention: abs value is applied multiplicatively for logarithmic axes! That means abs value=10 for a logarithmic axis adds log 10 to upper and/or lower axis limits.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that enlargelimits is applied before any changes to axis limits are considered as part of scale mode: enlargelimits will always be applied. Afterwards, the choice scale mode=scale uniformly will enlarge limits once more in order to satisfy all scaling constraints. The two limit enlargements are independent of each other, i.e. even if you say enlargelimits=false, scale mode will still increase axis limits if this seems to be necessary. An exception for this rule is enlarge-by-dimension, i.e. something like abs=1cm (see enlargelimits respects figure size for this case). See scale mode (especially scale mode=units only) and unit rescale keep size for detail on how to disable limit enlargement caused by scale mode. /pgfplots/enlargelimits respects figure size=true|false (initially true)

A key which is only used for something like enlarge x limits={abs=1cm}, i.e. for enlarge-bydimension. It controls if pgfplots will try to respect width/height. You should probably always leave it as its default unless you run into problems.

Allows to choose which coordinate is the logical origin of a logarithmic plot (either for a particular axis or for all of them). The choice log origin=infty is probably useful for stacked plots: it denes the origin in log coordinates to be . To be compatibly with older versions, this is the default.

4.15. TICK OPTIONS

Can be used to interrupt updates of the data limits (for example, for single \addplot commands). This has the same eect as \pgfplotsinterruptdatabb ... \endpgfplotsinterruptdatabb.

\begin{pgfplotsinterruptdatabb} environment contents \end{pgfplotsinterruptdatabb} Everything in environment contents will not contribute to the data bounding box. The same eect can be achieved with update limits=false inside curly braces.

These values are not only the input : after the survey phase, their values will be overwritten with the resulting computed values. These may dier according to enlargelimits or scale mode. If you need to access them, you can write \pgfkeysvalueof{/pgfplots/xmin} somewhere in your code.

These options assign a list of positions where ticks shall be placed. The argument is either the empty string (which is the initial value), the command \empty, the special string data or a list of coordinates. The initial conguration of an empty string means to generate these positions automatically. The choice \empty will result in no tick at all. The special value data will produce tick marks at every coordinate of the rst plot. Otherwise, tick marks will be placed at every coordinate in coordinate list . The coordinate list will be used inside of a \foreach \x in { coordinate list } statement. The format is as follows: {0,1,2,5,8,1e1,1.5e1} (a series of coordinates), {0,...,5} (the same as {0,1,2,3,4,5}), {0,2,...,10} (the same as {0,2,4,6,8,10}), {9,...,3.5} (the same as {9, 8, 7, 6, 5, 4}), See [5, Section 34] for a more detailed denition of the options. Please be careful with white spaces inside of coordinate list (at least around the dots).

For logplots, pgfplots will apply log() to each element in coordinate list (similarly, any custom transformations are applied to the argument list).

Attention: You cant use the ... syntax if the elements are too large for TEX! For example, xtick=1.5e5,2e7,3e8 will work (because the elements are interpreted as strings, not as numbers), but xtick=1.5,3e5,...,1e10 will fail because it involves real number arithmetics beyond TEXs capacities. The default choice for tick positions in normal plots is to place a tick at each coordinate i h. The step size h depends on the axis scaling and the axis limits. It is chosen from a list of feasible step sizes such that neither too much nor too few ticks will be generated. The default for logplots is to place ticks at positions 10i in the axis range. The positions depend on the axis scaling and the dimensions of the picture. If log plots contain just one (or two) positions 10i in their limits, ticks will be placed at positions 10ih with feasible step sizes h as in the case of linear axis. The tick appearance can be (re)congured with\pgfplotsset{tick style={very thin,gray}}% \pgfplotsset{minor tick style={black}} % modifies the style every tick modifies the style every minor tick

These style commands can be used at any time. The tick line width can be congured with major tick length and minor tick length.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/minor /pgfplots/minor /pgfplots/minor /pgfplots/minor

(initially 0) (initially 0) (initially 0)

Sets the number of minor tick lines used either for single axes or for all of them. Minor ticks will be disabled if the major ticks dont have the same distance and they are currently only available for linear axes (not for logarithmic ones).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/minor /pgfplots/minor /pgfplots/minor /pgfplots/minor

Allows to provide a list of minor tick positions manually. The syntax is almost the same as for xtick or ytick: simply provide either a commaseparated list of tick positions or the special value data. An empty argument argument disables the minor tick feature (in contrast to xtick where the special value \empty clears the list and an empty argument causes pgfplots to compute a default tick list). In contrast to minor x tick num, this key allows to provide nonuniform minor tick positions.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.15. TICK OPTIONS

275

Adds additional tick positions and tick labels to the x or y axis. Additional tick positions do not aect the normal tick placement algorithms, they are drawn after the normal ticks. This has two benets: rst, you can add single, important tick positions without disabling the default tick label generation and second, you can draw tick labels on top of others, possibly using dierent style ags. 15% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Remarks: Use extra x ticks to highlight special tick positions. The use of extra x ticks does not aect minor tick/grid line generation, so you can place extra ticks at positions j 10i in logplots. Extra ticks are always typeset as major ticks. They are aected by major tick length or options like grid=major.

Use the style every extra x tick (every extra y tick) to congure the appearance. You can also use extra x tick style={ ... } which has the same eect.

/pgfplots/xtickten={ exponent base 10 list } /pgfplots/ytickten={ exponent base 10 list } /pgfplots/ztickten={ exponent base 10 list } These options allow to place ticks at selected positions 10k , k { exponent base 10 list }. They are only used for logplots. The syntax for { exponent base 10 list } is the same as above for xtick={ list } or ytick={ list }. Using xtickten={1,2,3,4} is equivalent to xtick={1e1,1e2,1e3,1e4}, but it requires fewer computational time and it allows to use the short syntax xtickten={1,...,4}.

In case log basis x= 10, the meaning of xtickten changes. In such a case, xtickten will still assign the exponent, but for the chosen log basis x instead of base 10. /pgfplots/xticklabels={ label list } /pgfplots/yticklabels={ label list } /pgfplots/zticklabels={ label list } Assigns a list of tick labels to each tick position. Tick positions are assigned using the xtick and ytick-options. This is one of two options to assign tick labels directly. The other option is xticklabel={ command } (or yticklabel={ command }). The option xticklabel oers higher exibility while xticklabels is easier to use. See also the variant xticklabels from table. The argument label list has the same format as for ticks, that meansxticklabels={$\frac{1}{2}$,$e$}

Note that it is also possible to terminate list entries with two backslashes, \\. In that case, the last entry needs to be terminated by \\ as well (it is the same alternative syntax which is also accepted for \legend and cycle list). Please keep in mind that the arguments always refer the a list of tick positions, although it does not alter or dene the list of positions. Consequently, you should also provide the list of positions. Note that a list of positions might be longer than what is actually displayed (in case the axis limits clip some of the value away), but the index mapping into label list still includes the clipped values. /pgfplots/xticklabel={ command } /pgfplots/yticklabel={ command } /pgfplots/zticklabel={ command } These keys change the TEX-command which creates the tick labels assigned to each tick position (see options xtick and ytick). This is one of the two options to assign tick labels directly. The other option is xticklabels={ label list } (or yticklabels={ label list }). The option xticklabel oers higher exibility while xticklabels is easier to use. The argument command can be any TEX-text. The following commands are valid inside of command : \tick The current element of option xtick (or ytick). \ticknum The current tick number, starting with 0 (it is a macro containing a number). \nexttick This command is only valid if the x tick label as interval option is set (or the corresponding variable for y ). It will contain the position of the next tick position, that means the right boundary of the tick interval. The default argument is \axisdefaultticklabel for normal plots:\def\axisdefaultticklabel{$\pgfmathprintnumber{\tick}$}

\axisdefaultticklabellog for logplots:

That means you can congure the appearance of linear axis with the number formatting options described in Section 4.13 and logarithmic axis with log number format code, see below. The key yticklabel is a code fragment which is supposed to handle any incoming \tick value. Consequently, it can be used to append custom suxes or even units:

4.15. TICK OPTIONS

% Preamble: \pgfplotsset{width=7cm,compat=1.9}

279

100 10 1 0.1 0.01 6e 4e 2e 0e 2e 4e 6e

The following example uses explicitly formatted x tick labels and a small TEX script to format y tick labels as fractions in the form sign number /10 (note that the /pgf/number format/frac style can do similar things automatically, see PgfplotsTable and the documentation therein). A special Prewavelet11/10

CHAPTER 4. THE REFERENCE The TEX script takes the \tick macro as input and applies some logic. The \ifdim\tick pt<0pt means if dimension \tick pt < 0pt. The \ifdim is TEXs only way to compare real xed point numbers and the author did not want to invoke \pgfmath for this simple task. Since \ifdim expects a dimension, we have to use the pt sux which is compatible with \pgfmath. The result is that negative numbers, zero and positive numbers are typeset dierently. You can change the appearance of tick labels with\pgfplotsset{tick label style={ font=\tiny, /pgf/number format/sci}}% this modifies the every tick label style

A variant of xticklabels={ list } which uses each entry in the column named colname from a table as tick labels. The rst argument \table or lename can be either a loaded table macro (i.e. the result of \pgfplotstableread{ le name }{ \table }) or just a le name. The second argument can be a column name, a column alias or a create on use specication (see PgfplotsTable for the latter two). Furthermore, it can be [index] integer in which case integer is a column index. The behavior of xticklabels from table is the same as if the column colname would have been provided as comma separated list to xticklabels. This means the column can contain text, TEX macros or even math mode. If you have white spaces in your cells, enclose the complete cell in curly braces, {example cell}. The detailed input format for tables is discussed in \addplot table and in the documentation for PgfplotsTable.

true) true) true) true) true) true) both)

Enables/disables the small tick lines either for single axis or for all of them. Major ticks are those placed at the tick positions and minor ticks are between tick positions. Please note that minor ticks are automatically disabled if xtick is not a uniform range52 .

The key minor tick length={ dimen } congures the tick length for minor ticks while the major variant applies to major ticks. You can congure the appearance using the following styles:\pgfplotsset{every tick/.append style={color=black}} % \pgfplotsset{every minor tick/.append style={thin}} % \pgfplotsset{every major tick/.append style={thick}} % applies to major and minor ticks, applies only to minor ticks, applies only to major ticks.

There is also the style every tick which applies to both, major and minor ticks. /pgfplots/xtickmin={ coord } /pgfplots/ytickmin={ coord } /pgfplots/ztickmin={ coord }52 A

uniform list means the dierence between all elements is the same for linear axis or, for logarithmic axes, log(10).

Tick Alignment: Positions and Shifts

Allows to choose where to place the small tick lines. In the default conguration, this does also aect tick labels, see below. The tick pos style sets all of them to the same value (aliased by tickpos). This option is only useful for boxed axes. For x, the additional choices bottom and top can be used which are equivalent to left and right, respectively. Both are accepted for y . Changing tick pos will also aect the placement of tick labels. Note that it can also aect the axis lines key, although not all combinations make sense. Make sure the settings are consistent.

(initially (initially (initially (initially

default) default) default) default)

Allows to choose where to place tick labels. The choices left and right place tick labels either at the left or at the right side of the complete axis. The choice default uses the same setting as xtick pos (or ytick pos). This option is only useful for boxed axes keep it to default for non-boxed gures. The ticklabel pos style sets all three of them to the same value. For x, the additional choices bottom and top can be used which are equivalent to left and right, respectively. Both are accepted for x.

(initially (initially (initially (initially

empty) empty) empty) empty)

Shifts tick labels in direction of the outer unit normal of the axis by an amount of dimension . The ticklabel shift sets the same value for all axes. This is usually unnecessary as the anchor of a tick label already yields enough spacing in most cases.

/pgfplots/scaled /pgfplots/scaled /pgfplots/scaled /pgfplots/scaled

Allows to factor out common exponents in tick labels for linear axes. For example, if you have tick labels 20000, 40000 and 60000, you may want to save some space and write 2, 4, 6 with a separate factor 104 . Use scaled ticks=true to enable this feature. In case of true, tick scaling will be triggered if the data range is either too large or too small (see below).

215 52 42 32 22 12 103 Here, the sci subscript option simply saves space. In general, base 10:e will divide every tick by 10e . The eect is not limited by the too large or too small decisions mentioned above. The value real: num allows to divide every tick by a xed num . For example, the following plot is physically ranged from 0 to 2 , but the tick scaling algorithm is congured to divide every tick label by .

The key tick scale binop is described below, it is set initially to \cdot. A further not very useful example is shown below. Every x tick label has been divided by 2, every y tick label by 3. 3 33.33 (3, 9) 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The last option, scaled ticks=manual:{ label }{ code } allows even more customization. It allows full control over the displayed scaling label and the scaling code: label is used as-is inside of the tick scaling label while code is supposed to be a one-argument-macro which scales each tick. Example: +65 535 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The label can be arbitrary. It is completely in user control. The second argument, code is supposed to be a one-argument-macro in which #1 is the current tick position in oating point representation. The macro is expected to assign \pgfmathresult (as a number). The pgf manual [5] contains detailed documentation about its math engine. This feature may also be used do transform coordinates in case they cant be processed with pgfplots: transform them and supply a proper tick scaling method such that tick labels represent the original range. If label is empty, the tick scale label wont be drawn (and no space will be occupied). Tick scaling does not work for logarithmic axes. /pgfplots/xtick scale label code/.code={ ... } /pgfplots/ytick scale label code/.code={ ... } /pgfplots/ztick scale label code/.code={ ... } Allows to change the default code for scaled tick labels. The default is\pgfplotsset{ xtick scale label code/.code={$\cdot 10^{#1}$} }

and the initial value of tick scale binop is \cdot, but it can be changed to \times if desired. If the code is empty, no tick scale label will be drawn (and no space is consumed). /pgfplots/tick scale label code/.code={ ... } A style which sets xtick scale label code and those for y and z . /pgfplots/tick scale binop={ TEX math operator } Sets the binary operator used to display tick scale labels. 10 421

/pgfplots/scale ticks below exponent={ exponent }

(initially -1)

Allows ne tuning of the scaled ticks algorithm: if the axis limits are of magnitude 10e and e < exponent , the common prefactor 10e will be factored out. The default is /pgfplots/scale ticks above exponent={ exponent } (initially 3) Allows ne tuning of the scaled ticks algorithm: if the axis limits are of magnitude 10e and e > exponent , the common prefactor 10e will be factored out.

4.15.4

Tick Fine-Tuning(initially 35)

The tick placement algorithm depends on a number of parameters which can be tuned to get better results. /pgfplots/max space between ticks={ number } Congures the maximum space between adjacent ticks in full points. The sux pt has to be omitted and fractional numbers are not supported. /pgfplots/try min ticks={ number } (initially 4) Congures a loose lower bound on the number of ticks. It should be considered as a suggestion, not a tight limit. This number will increase the number of ticks if max space between ticks produces too few of them. The total number of ticks may still vary because not all fractional numbers in the axis range are valid tick positions. /pgfplots/try min ticks log={ number } The same as try min ticks, but for logarithmic axis. /pgfplots/tickwidth={ dimension } /pgfplots/major tick length={ dimension } Sets the length of major tick lines. It can be accessed using \pgfkeysvalueof{/pgfplots/major tick length}. /pgfplots/subtickwidth={ dimension } /pgfplots/minor tick length={ dimension } Sets the length of minor tick lines. It can be accessed using \pgfkeysvalueof{/pgfplots/minor tick length}. /pgfplots/xtick placement tolerance /pgfplots/ytick placement tolerance /pgfplots/ztick placement tolerance (initially 0.05pt) (initially 0.05pt) (initially 0.05pt) (initially 0.1cm) (initially 0.1cm) (initially 0.15cm) (initially 0.15cm) (initially 3)

Tick lines and labels will be placed if they are no more than this tolerance beyond the axis limits. This threshold should be chosen such that it does not produce visible dierences while still providing fault tolerance. The threshold is given in paper units of the nal gure.

The initial setting is log basis x= which defaults to: the natural logarithm for any coordinates (basis exp(1)), and the logarithm base 10 for the display of tick labels. If the log basis is changed to something dierent than the empty string, the chosen logarithm will be applied to any input coordinate (if the axis scale is log as well) and tick labels will be displayed in this basis. In other words: usually, you see log axes base 10 and thats it. It is only interesting for coordinate lters: the initial setting (with empty number ) uses coordinate lists basis e although the display will use basis 10 (i.e. it is rescaled). Any non-empty value number causes both, coordinate lists and display to use number as basis for the logarithm. The javascript code of the clickable library will always use the display basis (which is usally 10) when it computes slopes. Technical remarks. When log basis x is used, the style log basis ticks={ axis char } will be installed (in this case log basis ticks=x). This style in turn will change log number format code. Please note that xtickten will be used dierently now: it will provide the desired ticks in the new basis! Despite the misleading name ten, xtickten={1,2,3,4} will yield ticks at 21 , 22 , 23 , 24 if log basis x=2 has been set.

Grid lines will be drawn before tick lines are processed, so ticks will be drawn on top of grid lines. You can congure the appearance of grid lines with the styles\pgfplotsset{grid style={help lines}} % modifies the style every axis grid \pgfplotsset{minor grid style={color=blue}} % modifies the style every minor grid \pgfplotsset{major grid style={thick}} % modifies the style every major grid

4.17

Custom Annotations

Often, one may want to add custom drawing elements or descriptive texts to an axis. These graphical elements should be associated to some logical coordinate, grid point, or perhaps they should just be placed somewhere into the axis. pgfplots assists with the following ways when it comes to annotations: 1. You can explicitly provide any Tik Z instruction like \draw ... allows to provide coordinates of pgfplots. ; into the axis. Here, the axis cs

Furthermore, rel axis cs allows to position Tik Z elements relatively (like 50% of the axis width). 2. pgfplots can automatically generate nodes at every coordinate using its nodes near coords feature. 3. pgfplots allows you to place nodes on a plot, using the \addplot ... feature. node[pos= fraction ] {};

This section explains all of the approaches, except for the nodes near coords feature which is documented in its own section.

290

CHAPTER 4. THE REFERENCE

4.17.1

Accessing Axis Coordinates in Graphical Elements

Coordinate system axis cs pgfplots provides a new coordinate system for use inside of an axis, the axis coordinate system, axis cs. It can be used to draw any Tik Z-graphics at axis coordinates. It is used like\draw (axis cs:18943,2.873391e-05) |- (axis cs:47103,8.437499e-06);

102 103 Dof

Whenever you draw additional graphics, consider using axis cs! It applies any custom transformations (including symbolic x coords), logarithms, data scaling transformations or whatever pgfplots usually does and provides a low level pgf coordinate as result. In case you need only one component (say, the y component) of such a vector, you can use the \pgfplotstransformcoordinatey command, see Section 8.4 for details about basic level access.

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291

The result of axis cs is always an absoute position inside of an axis. This means, in particular, that adding two points has unexpected eects: the expression (axis cs:0,0) ++ (axis cs:1,0) is not necessarily the same as (axis cs:1,0). The background for such unexpected eects is that pgfplots applies a shifted linear transformation which moves the origin in order to support its high accuracy and high data range (compare the documentation of disabledatascaling). In order to express relative positions (or lengths), you need to use axis direction cs. Coordinate system axis direction cs While axis cs allows to supply absolute positions, axis direction cs supplies directions. It allows to express relative positions, includings lengths and dimensions, by means of axis coordinates. As noted in the documentation for axis cs, adding two coordinates by means of the Tik Z ++ operator may have unexpected eects. The correct way for ++ operations is axis direction cs: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0 1,000 1,200 1,400 1,600 1,800 2,000

Here, the target of the red arrow is the position (axis cs:2000,0) as expected. Using relative positions is mainly useful for linear axes. Applying this command to log-axes might still work, but it requires more care. One use-case is to supply lengths for example in order to support circle or ellipse paths. The correct way to draw an ellipse in pgfplots would be to specify the two involved radii by means of two (axis direction cs: x,y ) expressions. In general, this is possible if you use the basic level macros \pgfpathellipse and \pgfplotspointaxisdirectionxy. Please refer to the documentation of \pgfplotspointaxisdirectionxy for two examples of drawing arbitrary ellipses by means of this method. Since drawing circles and ellipses inside of an axis is a common use-case, pgfplots automatically communicates its coordinate system transformations to Tik Z: whenever you write \draw ellipse[x radius= x ,y radius= y ], the arguments x and y are considered to be pgfplots direction vectors and are handed over to axis direction cs. Consequently, ellipses with axis parallel radii are straightforward and use the normal Tik Z syntax:

Here, the two ellipses are specied as usual in Tik Z. pgfplots ensures that all necessary transformations are applied to the two radii. Note that pgfplots usually has dierent axis scales for x and y . As a consequence, the rotated red ellipse does not t into the axis lines; we would need to use axis equal to allow properly rotated ellipses. Attention: this modication to circles and ellipses requires \pgfplotsset{compat=1.5.1}.

The same applies to circles: in the standard view, a circle with radius=r will appear as an ellipse due to the dierent axis scales. Supplying axis equal results in true circles:1 % Preamble: \pgfplotsset{width=7cm,compat=1.9}

In case you need access to axis direction cs inside of math expressions, you can employ the additional math function transformdirectionx. It does the same as axis direction cs, but only in x direction. The result of transformdirectionx is a dimensionless unit which can be interpreted relative to the current pgf x unit vector ex (see the documentation of \pgfplotstransformdirectionx for details). There are the math commands transformdirectionx, transformdirectiony, and (if the axis is three dimensional) transformdirectionz. Each of them denes \pgfmathresult to contain the result of \pgfplotstransformdirectionx (or its variants for y and z , respectively).

4.17. CUSTOM ANNOTATIONS Coordinate system rel axis cs

293

The relative axis coordinate system, rel axis cs, uses the complete axis vectors as units. That means x = 0 denotes the point on the lower x axis range and x = 1 the point on the upper x axis range (see the remark below for x dir=reverse).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Points identied by rel axis cs use the syntax (rel axis cs: x , y ) or (rel axis cs: x , y , z ) where x , y and z are coordinates or constant mathematical expressions. The second syntax is only available in three dimensional axes. There is one specialty: if you reverse an axis (with x dir=reverse), points provided by rel axis cs will be unaected by the axis reversal. This is intended to provide consistent placement even for reversed axes. Use allow reversal of rel axis cs=false to disable this feature. There is also a lowlevel interface to access the transformations and coordinates, see Section 8 on page 445. Predened node current plot begin This coordinate will be dened for every plot and can be used is trailing path commands or after a plot. It is the rst coordinate of the current plot. Predened node current plot end This coordinate will be dened for every plot. It is the last coordinate of the current plot. /pgfplots/allow reversal of rel axis cs=true|false (initially true)

A ne-tuning key which species how to deal with x dir=reverse and rel axis cs and ticklabel cs.

The initial conguration true means that points placed with rel axis cs and/or ticklabel cs will be at the same position inside of the axes even if its ordering has been reversed. The choice false will disable the special treatment of x dir=reverse.

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4.17.2

Placing Nodes on Coordinates of a Plot

The \addplot command is not only used for pgfplots, it can also carry additional drawing instructions which are handed over to Tik Z after the plots path is complete. Among others, this can be used to add further nodes on the path. /tikz/pos={ fraction } The fraction identies a part of the recently completed plot if it is used before the trailing semicolon: 1 /2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the [yshift=8pt] tells Tik Z to shift all following nodes upwards. The node[pos=0] {$0$} instruction tells Tik Z to add a text node at 0% of the recently completed plot. The relative position 0% (pos=0) refers to the rst coordinate which has been seen by pgfplots, and 100% (pos=1) refers to the last coordinate. Any value between 0 and 1 is interpolated in-between. Note that all these nodes belong to the plots visualization (which is terminated by the semicolon). Consequently, all these nodes inherit the same graphic settings (like color choices). The position on the plot is computed by pgfplots using logical coordinates. That means: it computes the overall length of the curve before the curve is projected to screen coordinates and identies the desired position53 . Afterwards, it projects the nal position to screen coordinates. Thus, the position identies a location on the plot which is always the same, even in case of a rotated three-dimensional axis. pgfplots will linearly interpolate the fraction between successive coordinates. Valid choices for fraction are any numbers in the range [0, 1]. Note that the precise meaning of pos depends on the current plot handler: for most plot handlers, it defaults to linear interpolation (as in the examples above). For only marks, scatter, ybar, xbar, ybar interval, and xbar interval, it snaps to the nearest encountered coordinate. In this context, snap to nearest means that pos=p refers to the coordinate with index i = round(p N ) where N is the total number of points: Snap to nearest for scatter plots 1 3 0.5 2 0.3 1 0.1 0.2 0 0 0 1 2 3 0.4 0.75% Preamble: \pgfplotsset{width=7cm,compat=1.9}

the previous example shows that pos=p maps to one of the four available coordinates, namely the one53 This

can be a time-consuming process. Consider using the external library if you have lots of such gures.

4.17. CUSTOM ANNOTATIONS

295

whose index is closest to p N . Note that in such a case, the distance between coordinates is irrelevant only the coordinate index counts. Note that the fact that pgfplots uses logical coordinates to compute the target positions can produce unexpected eects if x and y axis operate on a dierent scales. Suppose, for example, that x is always of order 103 whereas y is of order 103 . In such a scenario, the y coordinate have no signicant contribution to the curves length although the rescaled axes clearly show signicant y dynamics. Consider using axis equal together with pos to produce comparable eects. /tikz/sloped (initially false)

Providing the Tik Z key sloped to a node identied by pos causes it to be rotated such that it adapts to the plots gradient. 1 /2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that the sequence in which sloped and shift transformations are applied is important: if shifts are applied rst (as would be the case without the every node/.style construction), the shifts do not respect the rotation. If sloped is applied rst, any subsequent shifts will be applied in the rotated coordinates. Thus, the case every node/.style={yshift=8pt} shifts every node by 8pt in direction of its normal vector. The sloped transformation is based on the gradient between two points (the two points adjacent to pos). Consequently, it inherits any sampling weaknesses. To see this, consider the example above with a dierent number of samples: 1

Here, the two extreme points have small slopes due to the sampling. While this does not seriously aect the quality of the plot, it has a huge impact on the transformation matrizes. Keep this in mind when you work with sloped (perhaps it even helps to add a further rotate argument). /tikz/allow upside down=true|false (initially false)

If /tikz/sloped is enabled and one has some dicult line plot, the transformation may cause nodes to be drawn upside down. The default conguration allow upside down=false will switch the rotation matrix, whereas allow upside down allows this case. (initially empty)

/tikz/pos segment={ segment index }

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CHAPTER 4. THE REFERENCE Occasionally, one has a single plot which consists of multiple segments (like those generated by empty line=jump or contour prepared). The individual segments will typically have dierent lengths, so it is tedious to identify a position on one of these segments. If pos segment= segment index is non-empty, the key pos= fraction is interpreted relatively to the provided segment rather than the whole plot. The argument segment index is an integer, where 0 denotes the rst segment.1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 % Preamble: \pgfplotsset{width=7cm,compat=1.9}

This plot has four segments (which are generated automatically by the plot handler). The annotation nodes are placed on the third segment, where sloped causes them to be rotated, allow upside down improves the rendering of the 0, and every node/.style install a shift in direction of the normal vector (see the documentation of sloped for details). Occasionally, one wants to place a node using pos and one wants to typeset the coordinates of that point inside of the node. This can be accomplished using \pgfplotspointplotattime: \pgfplotspointplotattime \pgfplotspointplotattime{ fraction } This command is part of the pos={ fraction } implementation: it denes the current point of pgf to fraction of the current plot. Without an argument in curly braces, \pgfplotspointplotattime will take the current argument of the pos key. Thus, the command computes the basic pgf coordinates but it also returns the logical coordinates of the resulting point into the following keys: /data point/x /data point/y /data point/z (no value) (no value) (no value)

After \pgfplotspointplotattime returns, these macros contain the x, y , and z coordinates of the resulting point. They can be used by means of \pgfkeysvalueof{/data point/x}, for example.

In the example above, three nodes have been placed using dierent pos= arguments. Invoking \pgfplotspointplotattime inside of the associated nodes body checks if pos already has a value and uses that value. The third node displays the coordinates inside of a pin. Due to internals of Tik Z, the pin knows nothing about the pos=0.7 argument of its enclosing node, so we need to replicate the 0.7 argument for \pgfplotspointplotattime{0.7}. The /pgf/number format/relative=0 style causes the number printer to round relative to 100 (compare against the same example without this style). In case you have symbolic x coords (or any other x coord inv tafo which produces non-numeric results), the output stored in /data point/x will be the symbolic expression: 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

In that specic case, you have to avoid \pgfmathprintnumber since the argument is no number. Note that symbolic x coords cannot return fractions between, say, A and B as you would expect. However, the point will still be placed at the fractional position (unless you have a scatter or bar plot). The computation of coordinates for the pos feature is computationally expensive for plots with many points. To reduce time, pgfplots will cache computed values: invoking the command \pgfplotspointplotattime multiple times with the same argument will reuse the computed value.

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4.17.3

Placing Decorations on Top of a Plot

Tik Z comes with the powerful decorations library (or better: set of libraries). Decorations allow to replace or extend an existing path by means of fancy additional graphics. An introduction into the decorations functionality of Tik Z is beyond the scope of this manual and the interested reader should read the associated section in [5]. This section shows how to use decorations to enhance plots in pgfplots. Suppose you have some graphics for which you would like to add direction pointers: Undecorated Graphics% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Our aim is to add short pointers indicating the direction of the parameterization. The solution is to use \usetikzlibrary{decorations.markings} and a decoration inside of \addplot: Decorated Graphics% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The only changes are in the option list for \addplot: it contains a postaction={decorate} which activates the decoration (without replacing the original path) and some specication decoration containing details about how to decorate the path. A discussion of details of the decorations libraries is beyond the scope of this manual (see [5] for details), but the main point is to add the required decorations to \addplot and its option list.

4.18. STYLE OPTIONS

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4.184.18.1

Style OptionsAll Supported Styles

pgfplots provides many styles to customize its appearance and behavior. They can be dened and changed in any place where keys are allowed. Furthermore, own styles are dened easily. Key handler key /.style={ key-value-list } Denes or redenes a style key . A style is a normal key which will set all options in key-value-list when it is set. Use \pgfplotsset{ key /.style={ key-value-list }} to (re)dene a style key in the namespace /pgfplots. Key handler key /.append style={ key-value-list } Appends key-value-list to an already existing style key . This is the preferred method to change the predened styles: if you only append, you maintain compatibility with future versions. Use \pgfplotsset{ key /.append style={ key-value-list }} to append key-value-list to the style key . This will assume the prex /pgfplots.

Styles installed for linear/logarithmic axis

/pgfplots/every axis (style, initially empty) Installed at the beginning of every axis. Tik Z options inside of it will be used for anything inside of the axis rectangle and any axis descriptions. /pgfplots/every axis post (style, initially empty) A style which is applied right after arguments provided to an axis are processed. In the following example, such a style is used to override the xmin and xmax options provided as arguments to \begin{axis}[...]:\begin{tikzpicture} \pgfplotsset{ every axis post/.style={ xmin=0,xmax=1, }, } \begin{axis}[ xmin=-1,xmax=2, ymin=0,ymax=1] ... \end{axis} \end{tikzpicture}

It is processed right after the arguments of \begin{axis}, but before styles like yticklabel style etc. are evaluated. /pgfplots/every semilogx axis (style, initially empty) (style, initially empty) (style, initially empty) (style, initially empty) Installed at the beginning of every plot with linear x axis and logarithmic y axis, but after every axis. /pgfplots/every semilogy axis Likewise, but with interchanged roles for x and y . /pgfplots/every loglog axis Installed at the beginning of every loglog plot. /pgfplots/every linear axis Installed at the beginning of every plot with normal axis scaling.

Styles installed for single plots

/pgfplots/every axis plot (style, initially empty) Installed for each plot. This style may contain options like samples, gnuplot parameters, error bars and it may contain options which aect the nal drawing commands.

300 /pgfplots/every axis plot post

CHAPTER 4. THE REFERENCE (style, initially empty)

This style is similar to every axis plot in that is applies to any drawing command in \addplot. However, it is set after any user dened styles or cycle list options.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

4.18. STYLE OPTIONS /pgfplots/every axis title The initial setting is

\pgfplotsset{every axis title/.style={at={(0.5,1)},above,yshift=6pt}}

301 (style, no value)

Used for any axis title. The at=( x,y ) syntax will place the title using axis description cs.

To be more precise, the yshift doesnt use the hardcoded 6pt: it uses the value of /pgfplots/every axis title shift={ default shift } which can be reset if needed. /pgfplots/title style={ key-value-list } An abbreviation for every axis title/.append style={ key-value-list }. It appends options to the already existing style every axis title. /pgfplots/every axis legend (style, no value) (initially 6pt)

Allows to change the appearance of the small legend images after the options of the plot style have been applied. Thus, legend formatting can be changed independently of the plot style using every legend image post. This key is also documented on page 204. /pgfplots/legend image post style={ key-value-list } An abbreviation for every legend image post/.append style={ key-value-list }. It appends options to the already existing style every legend image post. /pgfplots/every legend to name picture A style for use with legend to image, see the documentation therein. /pgfplots/every colorbar (style, no value) (style, no value)

A style to change the colorbar. See page 225 for the reference documentation of every colorbar. /pgfplots/colorbar style={ key-value-list } An abbreviation for every colorbar/.append style={ key-value-list }. It appends options to the already existing style every colorbar.

Styles for axis lines

302 /pgfplots/every outer z axis line Installed for every axis line which lies on the outer box.

CHAPTER 4. THE REFERENCE (style, initially empty)

If you want arrow heads, you may also need to check the separate axis lines boolean key. /pgfplots/every inner x axis line /pgfplots/every inner y axis line /pgfplots/every inner z axis line Installed for every axis line which is drawn using the center or middle options. /pgfplots/axis line style={ key-value-list } /pgfplots/inner axis line style={ key-value-list } /pgfplots/outer axis line style={ key-value-list } /pgfplots/x axis line style={ key-value-list } /pgfplots/y axis line style={ key-value-list } /pgfplots/z axis line style={ key-value-list } These options modify parts of the axis line styles. They append options to every inner x axis line and every outer x axis line and the respective y /z variants. Please refer to Section 4.9.9 on page 216 for details about styles for axis lines. /pgfplots/every 3d box foreground (style, no value) (style, initially empty) (style, initially empty) (style, initially empty)

Installed for the parts drawn by 3d box=complete. This aects axis lines, tick lines and grid lines drawn in the foreground. The background drawing operations have already been done when this style is evaluated. /pgfplots/3d box foreground style={ key-value-list } An abbreviation for every 3d box foreground/.append style={ key-value-list }. It appends options to the already existing style every 3d box foreground. /pgfplots/every colorbar sampled line (style, no value)

To be used in conjunction with colorbar sampled line, see the documentation therein. /pgfplots/colorbar sampled line style={ key-value-list } An abbreviation for every colorbar sampled line/.append style={ key-value-list }. It appends options to the already existing style every colorbar sampled line.

Styles for ticks

/pgfplots/every tick Installed for each of the small tick lines. /pgfplots/tick style={ key-value-list } An abbreviation for every tick/.append style={ key-value-list }. It appends options to the already existing style every tick. /pgfplots/every minor tick Used for each minor tick line, installed after every tick. /pgfplots/minor tick style={ key-value-list } An abbreviation for every minor tick/.append style={ key-value-list }. It appends options to the already existing style every minor tick. /pgfplots/every major tick Used for each major tick line, installed after every tick. /pgfplots/major tick style={ key-value-list } An abbreviation for every major tick/.append style={ key-value-list }. It appends options to the already existing style every major tick. (style, initially empty) (style, initially empty) (style, initially very thin,gray)

Allows to congure the appearance of extra x ticks. This style is installed before touching the rst extra x tick. It is possible to set any option which aects tick or grid line generation. The initial setting is\pgfplotsset{ every extra x tick/.style={/pgfplots/log identify minor tick positions=true}, every extra y tick/.style={/pgfplots/log identify minor tick positions=true}}

(Re)Dening Own Styles

Use \pgfplotsset{ style name /.style={ key-value-list }} to create own styles. If style name exists already, it will be replaced. Please note that it is not possible to use the Tik Z-command \tikzstyle{ style name }=[] in this context54 .

0 0 0.2 0.4 0.6 0.8 1

4.194.19.1

Alignment OptionsBasic Alignment

Alignment works with two main methods: a coordinate where the axis shall be drawn and an anchor inside of the axis which shall be drawn at this particular coordinate. This methodology is common for each Tik Z node and an axis is nothing but a (special) Tik Z node. The coordinate can be specied using the at54 This was possible in a previous version and is still supported for backwards compatibility. But in some cases, it may not work as expected.

4.19. ALIGNMENT OPTIONS

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key, while the anchor can be specied with the anchor key. In most cases, it is sucient to provide only an anchor unless one needs more than one axis in the same picture environment. /pgfplots/at={ coordinate expression } Assigns a position for the complete axis image. This option works similarly to the at-option of \node[at={ coordinate expression }], see [5]. The common syntax is at={( x,y )}. The idea is to provide an coordinate expression where the axis will be placed. The axis anchor will be placed at coordinate expression . /pgfplots/anchor={ name } (initially south west)

Chooses one of the dierent possible positions inside of an axis which is placed with at. The at key denes the position where to place the axis inside of the embedding picture, the anchor key denes which point of the axis shall be positioned by at. The initial conguration assumes at={(0,0)}. Thus, anchor=center will place the axis center at the logical picture position (0, 0). Similarly, anchor=south west will position the lower left corner of the axis at (0, 0). For users who are familiar with Tik Z: an axis is actually a very special node, so anchors work as in [5]. Anchors are useful in conjunction with horizontal or vertical alignment of plots, see the examples below. There are four sets of anchors available: anchors positioned on the axis bounding box, anchors on the outer bounding box and anchors which have one coordinate on the outer bounding box and the other one at a position of the axis rectangle. Finally, one can place anchors near the origin. In more detail, we have anchors on the axis rectangle (the bounding box around the axis)55 ,(s.north west) (s.north)

10 2(s.west)

A test plot.

(s.north east)

(s.center)

f (x) g ( x)(s.east)

0 2 4 40 20 0 20 (s.south) x 40

(s.south west)

(s.south east)

Anchors on the outer bounding box,

(s.outer north west) (s.outer north) (s.outer north east)

104 2 0

A test plot. f (x) g ( x)

(s.outer east)

(s.outer center)

(s.outer west)

2 4 40 20 0 x 20 40

(s.outer south west)

(s.outer south)

(s.outer south east)

There are anchors which have one coordinate on the outer bounding box, and one on the axis rectangle,55 Versions prior to pgfplots v.1.3 did not use the bounding box of the axis, they used axis coordinates to orient these anchors. This has been xed. If you really want to undo the bugx, see compat/anchors.

308(s.above north west) (s.above north)

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(s.above north east)

(s.left of north west)

104 2 0 2

A test plot.(s.right of north east)

f (x) g ( x)(s.right of east)

(s.left of west)

(s.left of south west)

(s.right of south east)

40 20 0 x

20

40

(s.below south west)

(s.below south)

(s.below south east)

And nally, we have origin anchors which are especially useful when axis lines pass through the origin,(s.above origin)

100 y

50(s.left of origin) (s.origin) (s.right of origin)

2(s.below origin)

There is a fth anchor which is not directly related to the axis: you can provide the anchor of a named inner node. Thus, you can dene your own anchor, by writing \node ( name ) at ( point coordinate ) {}; as follows (using the baseline option described below):1 0.5(aninnernode)

What happens is that a node is placed at (axis cs:-2,0.75). Note that the options [pin=...] are merely to show the \node (the pin style has been dened by the pgfplots manual). Since a name can also be assigned using name= nodes name and since any pgfplots description is also a \node, you can align your plot at selected axis descriptions:

The default value is anchor=south west. You can use anchors in conjunction with the Tik Z baseline option and/or \begin{pgfinterruptboundingbox} to perform alignment. Remarks: Each of the anchors on the axis rectangle has an equivalent to a coordinate in the axis description cs described in Section 4.9.1. That means the rst set of anchors actually lives on the tight bounding box around the axis (without any ticks or descriptions). The south west anchor will always be the lower left corner of this bounding box, even in case of a rotated or skewed coordinate system56 . Similar statements hold for the other anchors.

4.19.2

Vertical Alignment with baseline

(no value)

/tikz/baseline

The baseline option should be provided as argument to a tikzpicture. It congures Tik Z to shift the picture position y = 0 to the embedding texts baseline: This is a picture, here another one.

This is \tikz[baseline]\fill[red] (0,0) circle(3pt); a picture, here \tikz[baseline]\fill[red] (0,10pt) circle(3pt); another one.

Consequently, the baseline option allows to align dierent tikzpictures. An axis is, by default, placed with at={(0,0)}, and the anchor key species which part of the axis is placed at (0,0). Consequently, the baseline option, together with anchor, allows to align dierent axes with the embedding text. The default axis anchor is south west, which means that the picture coordinate (0, 0) is the lower left corner of the axis. As a consequence, the Tik Z option baseline allows vertical alignment of adjacent plots:56 Note

Note that it is also possible to write baseline=5cm in which case the image oset at y =5cm will be used as baseline. The baseline key is related to \begin{minipage}[ alignment ] or \begin{tabular}[ alignment ]:

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A the alignment tells L TEX which part of the minipage or tabular shall be positioned on the baseline. Thus, baseline does the same for pictures (with more freedom for alignment ).

4.19.3

Horizontal Alignment

Horizontal alignment can be done in two ways: 1. Using separate tikzpicture environments which have reduced bounding boxes or 2. A single tikzpicture environment in which the complete alignment is done. The rst approach requires the use of reduced bounding boxes and is discussed in Section 4.20.1. The second approach, a single tikzpicture environment, employs the at and anchor keys to align parts of the images. For example, if you place multiple axes into a single tikzpicture and use the anchor-option, you can control horizontal alignment: 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the second axis uses at={(main plot.below south west)} to be placed below the rst one. Furthermore, it has yshift=-0.1cm in order to leave additional space, and it uses anchor=north west to place the upper left corner at the specied position. Instead of the at={} construction, we could also have used yshift with larger negative shift.

4.19.4

Alignment In Array Form (Subplots)

Sometimes multiple alignment axes in array form are desired. pgfplots supports this task in several ways which are described in the following. There are basically three related, yet dierent, approaches:A 1. Simply place \begin{tikzpicture}...\end{tikzpicture} into a L TEX table. This is straight forward; you would do the very same thing with \includegraphics. In addition to \includegraphics, the baseline feature allows simple yet eective vertical alignment. In addition, the trim left and trim right features allow simple yet eective horizontal alignment (see below).

2. Use a single picture which contains an array of axes, i.e. a pattern like

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CHAPTER 4. THE REFERENCE \begin{tikzpicture} \matrix{ multiple axes }; \end{tikzpicture}. This allows considerably simpler alignment! Alas, it needs special handling for legend entries due to a weakness of \matrix. If you use the external library (which is recommended), it takes more time since the picture gets larger. 3. Use the groupplots library shipped with pgfplots. It is specialized on axes in array form with particular strength if the axes are closely related (for example if they share axis descriptions like xlabel or even tick labels). Note, however, that the other approaches are better when it comes to automatic handling of bounding boxes. The groupplots library is discussed in all detail in Section 5.5. This section discusses the other two approaches.A A Array Alignment using L TEX Tables The idea is simple: use a L TEX table and provide one tikzpicture for every cell. You are probably familiar with this sort of alignment, perhaps together with \includegraphics. It works in the very same way for pgfplots. The approach is the simplest one since it doesnt need special knowledge. Its disadvantage, however, is more diculty to control positions inside of the image (like dierently sized axis descriptions).

Is is strongly recommended to employ the baseline option for each cell picture, which simplies vertical alignment considerably. If you want a simple solution to place separate axes in array form, and you prefer to use one tikzpicture for every axis, the probably most simple and most eective way to get horizontal alignment are the trim left and trim right features or styles based on them: The trim axis left feature can be used to exclude axis descriptions on the left from the bounding box, and the trim axis right can exclude axis descriptions on the right from the bounding box. Thus, alignment is done using the vertical axis lines. Since both keys eectively modify the bounding box, they are documented in Section 4.20.1 Bounding Box Restrictions. Here is just a small example for array alignment by means of tabular, baseline and the trim left/trim right features: Trimmed bounding boxes6 4 20 2 0 10 2 4 6 6 4 2 0 2 4 6 6 4 2 0 2 4 6 0

The example has 2 2 axes. The baseline feature controls the vertical alignment: the lower axis lines are always on the same height. The trim axis left key is a style which tells Tik Z to trim everything which is left of the left axis line. Similarly, the trim axis right key does not include picture parts right of the right axis line. Together with \begin{center} and the yticklabel pos=right key, we get correct horizontal and vertical alignment together with centering at the left- and right axis lines (without descriptions). A strong advantage is that this type of alignment requires almost no changes to your pictures. Thus, you can copypaste existing images (TEX code) relatively simple. Note that the approach is fully compatible with the image externalization library: each picture is exported separately, and the bounding box restrictions (and the baseline oset) are stored in separate .dpth les. The trim left/trim right approach for horizontal alignment is the only supported way for reduced bounding boxes and image externalization. Array Alignment using Tik Z Matrices While it is possible to use (for example) tabular combined with the vertical and horizontal alignment methods discussed above, it might be better to use a Tik Z matrix since it automatically handles the size of axis descriptions. A Tik Z matrix is some sort of graphical table. It knows everything about picture alignment and it has more exibility than tabular when it comes to graphics. The idea is to pack the complete array into a single picture. The complete documentation of a Tik Z matrix is beyond the scope of this manual, please refer to [5] for details. But we provide an example here:

So, a matrix is a picture element inside of tikzpicture. Its cells are separated by & as in tabular (or, if & causes problems, with \pgfmatrixnextcell). Its rows are separated by \\. Each cell is aligned using the cells anchor. Since, by default, the anchor of an axis is placed at the lower left corner, the example above is completely aligned, without the need for any bounding box modications even the labels are aligned correctly. If another anchor shall be used, simply place\pgfplotsset{anchor=....} \matrix { ... };

in front of the matrix. This will use the same conguration for every sub-plot.

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Attention: Unfortunately, the array alignment with \matrix needs special attention with legends. A legend is also a \matrix and Tik Z matrices cant be nested. You will need to use the legend to name feature (or to assemble a legend by means of \label and \ref) to overcome this weakness (see Section 4.9.6 for details).

4.19.5

Miscellaneous for Alignment

Predened node current axis A node which refers to the current axis or the last typeset axis. You can use this node in axis descriptions, for example to place axis labels or titles. Remark: If you use current axis inside of axis descriptions, the current axis is not yet nished. That means you cant use any outer anchor inside of axis descriptions. It is also possible to use current axis in any drawing or plotting commands inside of an axis (but no outer anchor as these are not dened when drawing commands are processed). This usage is similar to the axis description cs.

4.20

The Pictures Size: Bounding Box and Clipping

This section explains how a picture receives its nal dimensions. The pictures dimension is the bounding box. It is possible to restrict the bounding box, but display graphical elements outside of the bounding box. This is called subject of Section 4.20.1. Another use-case is to restrict both the bounding box and the clip the graphical elements to some outer path which is subject of Section 4.20.2.

4.20.1

Bounding Box Restrictions

Bounding box restrictions are a useful and often necessary tool if multiple pictures need to be aligned properly. Consequently, it is often applied together with the Alignments methods of Section 4.19. Bounding box restrictions can be archieved with several methods of pgf: 1. The overlay option, 2. The pgfinterruptboundingbox environment, 3. The \pgfresetboundingbox command, 4. The \useasboundingbox path, 5. The trim left and trim right feature (which is the only supported way of restricted bounding boxes and image externalization; at least for pdf output). An additional item is a specic use-case of pgfplots: 6. The hide axis feature will exclude any axisspecic stu from the bounding box. See the reference for hide axis for details. Note that image externalization (the external library) is more or less incompatible with methods (1.) (4.). The problem is that pdflatex crops everything outside of the bounding box away. There are only two safe ways to restrict bounding boxes of external .pdf images: the rst is the mentioned trim left/trim right feature and the second is to use negative \hspace or \vspace commands (or options to \includegraphics). /tikz/overlay (no value)

A special key of pgf which disables bounding box updates for (parts of) the image. The eect is that those parts are an overlay over the document. For pgfplots, overlay can be useful to position legends or other axis descriptions outside of the axis without aecting its size (and without aecting alignment). For example, one may want to include only certain parts of the axis into the nal bounding box. This would allow horizontal alignment (centering):

More information about the overlay option can be found in the pgf manual [5]. \pgfresetboundingbox This command of pgf resets the bounding box of the current picture. The computation starts from scratch afterwards, allowing to compute a userdened bounding box. A title% Preamble: \pgfplotsset{width=7cm,compat=1.9}

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The example draws a normal picture, containing an axis. Afterwards, it throws the bounding box away and creates a new one based on the current axis node and its anchors. \begin{pgfinterruptboundingbox} environment contents \end{pgfinterruptboundingbox} Yet another approach with the same eect is shown below: the bounding box is interrupted manually, and resumed afterwards. A title x2 10 y x3 x4% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The pgfinterruptboundingbox environment does not include its content into the images bounding box, and \useasboundingbox sets the pictures bounding box to the following argument (see [5]). /tikz/trim left={ x coordinate or point } /tikz/trim right={ x coordinate or point } These two keys allow to reduce the size of the bounding box. The trim left key expects either a single x coordinate like 1cm or a point like (current axis.west). If a point is provided, is uses only the x coordinate of that point. Then, the left end of the bounding box is set to the resulting x coordinate and everything left of it is outside of the bounding box. The trim right key has the same eect, only for the right end of the bounding box. More detailed documentation can be found in the Tik Z manual. /tikz/trim axis left A style with value trim left=(current axis.south west). The style needs to be provided as argument to \begin{tikzpicture}[trim axis left]. It expects (at least) one pgfplots environment in the picture. The eect is to trim everything which is left of the last axis anchor south west (i.e. everything left of the left axis boundary). /tikz/trim axis right A style with value trim right=(current axis.south east). It works similarly to trim axis left: the eect is that everything right of the right axis line of the last axis environment is truncated from the bounding box. /tikz/trim axis group left It has the value trim left=(group c1r1.south west). (style, no value) (style, no value) (style, no value) (default 0pt)

A style which has the same eect as trim axis left, but is tailored for the groupplots library.

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CHAPTER 4. THE REFERENCE The style needs to be provided as argument to \begin{tikzpicture}[trim axis group left]. It expects (at least) one groupplot environment in the picture. The eect is to trim everything which is left of the rst group axis anchor south west (i.e. everything left of the left axis boundary). /tikz/trim axis group right (style, no value)

A style which has the same eect as trim axis right, but is tailored for the groupplots library. It works similarly to trim axis group left: the eect is that everything right of the rightmost axis in a group plot (the last element of the groupplot environment) is truncated from the bounding box.

4.20.2

Clipping

Clipping incluences both the picture size and the visible output in contrast to bounding box restrictions which reduce the pictures nal size while keeping the same graphical output. Typically, pgfplots uses the path for a boxed axis as clip path. However, clipping has some special features and netuning keys which are explained in this section. /pgfplots/clip=true|false (initially true)

Controls whether any paths inside of an axis shall be clipped.

This is in eect even if hide axis=true. Note that a clip path can contribute to the pictures bounding box. Starting with compat=1.8, pgfplots applies intelligence to separate the responsabilities clipping and bounding box control, see clip bounding box and its choices. As of compat=1.8, a clip path can be in eect although the bounding box is considerably smaller than the clip path. This is typically what one expects if the clip path is invisible. The clip path is generated using \pgfplotspathaxisoutline, i.e. it is the path induced by boxed axis lines. For a threedimensional plot, only the outer axis lines are used. A plot with centered axis lines uses the outer axis lines as well. /pgfplots/clip marker paths=true|false (initially false)

The initial choice clip marker paths=false causes markers to be drawn after the clipped region. Only their positions will be clipped. As a consequence, markers will be drawn completely, or not at all. The value clip marker paths=true is here for backwards compatibility: it does not introduce special marker treatment, so markers may be drawn partially if they are close to the clipping boundary57 . This key has no eect if clip=false. Note that clip marker paths also aects the sequence in which plots and their markers are drawn on top of each other. See also the related key clip mode.

/pgfplots/clip bounding box=default tikz|upper bound

(initially controlled by compat key)

Controls how the path generated by clip=true contributes to the bounding box. This has a consequence for axis lines=box, in particular, for hide axis: if the value is default tikz, hiding (parts of) the axis will not reduce the bounding box because the clip path is as large as before. The value upper bound allows to reduce the bounding box also in case of hide axis. More precisely, the choice default tikz installs the clip path induced by the axis as ordinary Tik Z path (see \pgfplotspathaxisoutline). That means its bounding box essentially contributes to the pictures bounding box, irrespective of the size of contained paths.

The choice upper bound allows to reduce the pictures bounding box to what is actually shown: if the picture only contains graphical elements which are completely within the bounding box of \pgfplotspathaxisoutline, the bounding box is made up of those contained elements. If the contained elements are actually larger than the bounding box of \pgfplotspathaxisoutline, they are clipped to the outlines path (upper bound). The latter case ensures that parts of the graphics which are excluded by clip are not counted for the bounding box. Keep in mind that hide axis is independent of clip=true: the clip path might still be in eect even though the axis outline is invisible.57 Please

note that clipped marker paths may be slightly faster during TEX compilation.

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319

This key is irrelevant if clip=false. In addition, it has no eect for axis lines=box since the box path is made up from \pgfplotspathaxisoutline. It has an eect for hide axis=true or for choices of axis lines in which parts of the axis are empty. This key is controlled by the compat level. Its default is default tikz. Since compat=1.8, it is set to upper bound. The key has no eect if clip=false. /pgfplots/clip mode=global|individual (initially global)

This key controls how pgfplots implements the clip=true feature (which is on by default). Its primary motivation is control where markers are placed: are markers on top of everything else (choice global) or are they overdrawn by following plots (choice individual)? The choice global tells pgfplots to install one single clip path for the complete picture58 . In order to avoid clipped marker paths, any markers are processed after the clip path has been closed, i.e. on a separate layer (see clip marker paths). An unexpected sideeect is that marks are on top of plots, even if the plots have been added after the markers. The choice individual instructs pgfplots to install a separate clip path for every \addplot command. Consequently, the plot will be clipped. But most importantly, its markers will be drawn immediately after the clip path has been deactivated. An unexpected sideeect of clip mode=individual is that 1. the resulting pdf will be slightly larger due to the repeated paths, 2. custom drawing instruction like \node or \draw need to be clipped manually : use% Preamble: \pgfplotsset{width=7cm,compat=1.9}

to install a custom clip path around your \draw instructions for such a usecase. Here, the path instruction \pgfplotspathaxisoutline results in a path of the axis outline, i.e. the path which is used for the background paths or for clipping. Since it is a basic level macro, it needs to be encapsulated by \pgfextra. Note that clip marker paths can lead to the same result as clip mode=individual if the plot does not reach the boundaries.

4.21

Closing Plots (Filling the Area Under Plots)

\closedcycle Provide \closedcycle as trailing path commands after \addplot to draw a closed line from the last plot coordinate to the rst one. Use \closedcycle whenever you intend to ll the area under a plot.58 The

choice clip mode=global was the only supported clipping mechanism up to and including version 1.5.

Note that \closedcycle has been designed for functions (i.e. for a plot where every x has at most one y value). For arbitrary curves, you can safely use the Tik Z path --cycle instead which simply connects the last and the rst path element:59 The implementation for stacked plots requires some additional logic to determine the lled area: \closedcycle will produce a plot coordinates command with reversed coordinates of the previous plot. This is usually irrelevant for end users, but it assumes that the plots type is symmetric. Since constant plots are inherently asymmetric, \closedcycle will use const plot mark right as reversed sequence for const plot mark left.

The --cycle is actually a path instruction of [5]; it connects the rst and the last coordinate of one path. Note that this is automatically done for filled paths.

4.22

Symbolic Coordinates and User Transformations

pgfplots supports user transformations which can be applied to input and output coordinates. Suppose the plot shall display days versus account statements over time. Then, one wants to visualize date versus credit balance. But: dates need to be transformed to numbers before doing so! Furthermore, tick labels shall be displayed as dates as well. This, and more general transformations, can be implemented using the x coord trafo and y coord trafo keys. Remark: This section applies to users who want to have non-standard input coordinates. If you have normal numbers which dont need to be transformed and you like to have special symbols as tick labels, you should consider using the xticklabels (yticklabels) key described on page 277. See also Section 4.24.1 for dierent types of transformations and their interaction. /pgfplots/x coord trafo/.code={ ... }

CHAPTER 4. THE REFERENCE

These code keys allow arbitrary coordinate transformations which are applied to input coordinates and output tick labels. The x coord trafo and y coord trafo command keys take one argument which is the input coordinate. They are expected to set \pgfmathresult to the nal value. At this level, the input coordinate is provided as it is found in the \addplot statement. For example, if x coordinates are actually of the form year - month - day , for example 2008-01-05, then a useful coordinate transformation would transform this string into a number (see below for a predened realization). In short, no numerics has been applied to input coordinates when this transformation is applied60 . The input coordinate transformation is applied to any input coordinates (specied with \addplot or axis cs), any user-specied xtick or ytick options, any user-specied extra x ticks and extra y ticks options, any user-specied axis limits like xmin and xmax.

The output coordinate transformation x coord inv trafo is applied to tick positions just before evaluating the xticklabel and yticklabel keys. The argument to x coord inv trafo is a xed point number (which may have trailing zeros after the period). The tick label code may use additional macros dened by the inverse transformation. Remark: pgfplots will continue to produce tick positions as usual, no extra magic is applied. It may be necessary to provide tick positions explicitly if the default doesnt respect the coordinate space properly. The initial value of these keys is\pgfplotsset{ x coord trafo/.code={}, x coord inv trafo/.code={}}

which simply disables the transformation (the same for y , of course). Remark: It might be necessary to set

in order to avoid number formatting routines on \tick or numerics for tick scale methods. This is done automatically by the predened symbolic coordinate styles (see below).

4.22.1

String Symbols as Input Coordinates

It is possible to provide a string dictionary to pgfplots. An input coordinate can then use any symbol provided in that dictionary. /pgfplots/symbolic x coords={ dictionary } /pgfplots/symbolic y coords={ dictionary } /pgfplots/symbolic z coords={ dictionary } A style which sets x coord trafo and x coord inv trafo (or the respective y or z variants) such that any element in dictionary is a valid input coordinate. The dictionary can be a comma separated list60 Of

course, if coordinates have been generated by gnuplot or pgf, this does no longer hold.

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323

or a list terminated with \\. In both cases, white space is considered to be part of the names (use % at end of lines). The dictionary will assign integer numbers to every element. These integers are used internally for arithmetics. Finally, the inverse transformation takes a xed point number and maps it to the nearest integer, and that integer is mapped into the dictionary.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The eect of the transformation is simply that input coordinates can be elements of the dictionary and tick labels will be chosen out of this dictionary as well. Note that symbolic x coords is more-or-less equivalent to explicitly provided xtick positions and xticklabels:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The dierence is that the approach with symbolic x coords is simpler to read whereas the xtick approach is simpler with respect to coordinate arithmetics (for example to increase limits using enlargelimits). The xticklabel style here is an attempt to align all tick labels at their base line (which would be useful for symbolic x coords as well as soon as labels have characters which exceed the baseline). See also the option to add tick and/or grid lines at every encountered coordinate using xtick=data (or minor xtick=data).

4.22.2

Dates as Input Coordinates

The already mentioned application of using dates as input coordinates has been predened, together with support for hours and minutes. It relies on the pgf calendar library which converts dates to numbers in the Julian calendar. Then, one coordinate unit is one day.A \usepgfplotslibrary{dateplot} % L TEX and plain TEX \usepgfplotslibrary[dateplot] % ConTEXt A \usetikzlibrary{pgfplots.dateplot} % L TEX and plain TEX

CHAPTER 4. THE REFERENCE

Installs x coord trafo and x coord inv trafo (or the respective variant for coordinate ) such that ISO dates of the form year - month - day are accepted. Here, coordinate is usually one of x, y, or z, but it can also contain stu like hist/data. After installing this style, input values like 2006-02-28 will be converted to an appropriate integer using the Julian calender. Input coordinates may be of the form year - month - day or they may contain times as year - month - day hour : minute . The result of the transformation are numbers where one unit is one day and times are fractional numbers. The transformation is implemented using the pgf-calendar module, see [5, Calendar Library]. This reference also contains more information about extended syntax options for dates. The inverse transformation provides the following macros which are available during tick label evaluation (i.e. when used inside of xticklabel or yticklabel): \year expands to the year component, \month expands to the month component, \day expands to the day component, \hour expands to the hour component (using two digits), \Hour expands to the hour component (but omits leading zeros), \minute expands to the minute component (two digits), \Minute expands to the minute component (omits leadings zeros), \lowlevel expands to the low level number representing the tick, \second will always be 00.

Attention: If you intend to use hours and minutes, you should always provide the date ZERO to maintain adequate precision! /pgfplots/date ZERO= year - month - day (initially 2006-01-01)

A technical key which denes the 0 coordinate of date coordinates in. Users will never see the resulting numbers, so one probably never needs to change it. However, the resulting numbers may become very large and a mantisse of 6 signicant digits may not be enough to get accurate results. In this case, date ZERO should be set to a number which falls into the input date range.

4.23

Skipping Or Changing Coordinates Filters

pgfplots oers lters. A lter expects a (numeric) input coordinate and is allows to modify the coordinate or throw it away. Filters can either operate on individual coordinates or on all simultaneously. See also Section 4.24.1 for dierent types of transformations and their interaction. /pgfplots/x filter/.code={ ... } /pgfplots/y filter/.code={ ... } /pgfplots/z filter/.code={ ... }

326 /pgfplots/filter point/.code={ ... }

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The code keys x filter and y filter allow coordinate ltering which are based on a single coordinate. A coordinate lter gets an input coordinate as #1 (on input, the same value is stored in \pgfmathresult), applies some operation and writes the result into the macro \pgfmathresult. If \pgfmathresult is empty afterwards, the coordinate is discarded. You can also set \pgfmathresult to nan or inf in which case the coordinate can be either discarded (if unbounded coords=discard is set) or the plot can be interrupted (the case unbounded coords=jump). The filter point/.code lter allows ltering depending on all components forming a complete point (x, y and z ); it is described below. It is allowed that lters do not change \pgfmathresult. In this case, the unltered coordinate will be used. Coordinate lters are useful in automatic processing system, where pgfplots is used to display automatically generated plots. You may not want to lter your coordinates by hand, so these options provide a tool to do this automatically. The following lter adds 0.5 to every x coordinate. 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

0 4.5 5 5.5 6 6.5

Please refer to [5, pgfmath manual] for details about the math engine of pgf. Please keep in mind that the math engine works with limited TEX precision. During evaluation of the lter, the macro \coordindex contains the number of the current coordinate (starting with 0). Thus, the following lter discards all coordinates after the 5th and before the 10th.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

There is also a style key which simplies selection by index, see below. pgfplots invokes the lter with argument #1 set to the input coordinate. For x-lters, this is the x-coordinate as it is specied to \addplot, for y -lters it is the y -coordinate. If the corresponding axis is logarithmic, #1 is the logarithm (see log basis x and its variants) of the coordinate as a real number, for example #1=4.2341. In case the logarithm was undened, the argument will be empty. The arguments to coordinate lters are minimally preprocessed: rst, for logarithmic axes, the log of the argument is supplied. Second, any high level coordinate maps like x coord trafo (which may be

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used to map dates to numbers or string to numbers or so) are applied. In consequence, the #1 argument is supposed to be a number. No further transformation has been applied. Occasionally, it might be handy to get the raw, completely unprocessed input coordinate as it has been reported by the coordinate input routine. This unprocessed data is available in the three math parser constants rawx, rawy and rawz. All these values are ready for use in lters (and some other methods inuence plots as well). Note that rawy is to be used like a function without arguments, i.e. lters can employ it where math parsing is done. An application could be to lter log values based on the normal scale:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The preceding example uses rawy to throw all samples outside of the range [1, 15] away. If key lters are invoked for plot table, access to the current rows data can be achieved using \thisrow{ column name } (and its variants). This includes all columns of the table. The filter point key is more technical. It doesnt take an argument: its arguments are given in terms of the pgfkeys variables /data point x, /data point y and /data point z. It may change its coordinates using \pgfkeyssetvalue{/data point x}{ new value }; access to variables can be accessed with \pgfkeysvalueof{/data point/x} or, if the argument shall be written into a macro, with \pgfkeysgetvalue. This lter is evaluated after the other ones. Note that you can provide dierent x filter/y filter arguments to each \addplot command. It seems there are only problems with the #1 argument, and I havent yet found out why. Please use \pgfmathresult in place of #1 if you provide \addplot[x filter/.code={...}]. /pgfplots/pre filter/.code={ ... } Applied before x filter, y filter, and z filter. /pgfplots/skip coords between index={ begin }{ end } A style which appends an x filter which discards selected coordinates. The selection is done by index where indexing starts with 0, see \coordindex. Every coordinate with index begin i < end will be skipped.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE Technical note : this style usually applies to x coordinates (i.e. it counts x coordinates). In case you want to apply it to something like hist/data or quiver/u, you can 1. append an asterisk * to the styles name and 2. provide the target coordinates name as rst argument. For example, skip coords between index*={hist/data}{2} applies to hist/data.

/pgfplots/each nth point={ integer } A style which appends an x filter which discards all but each nth input coordinate. This downsampling works fairly well. It can be used to reduce a huge amount of coordinates from an input le. In this case, you should also set filter discard warning=false to avoid repeated notications about skipped coordinates and unbounded coords=discard such that pgfplots should silently forget any discarded points (rather than generated interrupted plots). Note that there is also a mark repeat style which applies the same operation to plot marks only. Technical note : this style usually applies to x coordinates (i.e. it counts x coordinates). In case you want to apply it to something like hist/data or quiver/u, you can 1. append an asterisk * to the styles name and 2. provide the target coordinates name as rst argument. For example, each nth point*={hist/data}{2} applies to hist/data. /pgfplots/restrict /pgfplots/restrict /pgfplots/restrict /pgfplots/restrict /pgfplots/restrict /pgfplots/restrict x y z x y z to to to to to to domain= min : max domain= min : max domain= min : max domain*= min : max domain*= min : max domain*= min : max

These keys append x (or y or z ) coordinate lters to restrict the respective coordinate to a domain. The versions without star (like restrict x to domain) will assign the value -inf if the coordinate is below min and +inf if the coordinate is above max . The starred versions (like restrict x to domain*) will truncate coordinates to [ min , max ], i.e. they assign the value min if the coordinate falls outside of the lower limit and max if the value falls outside of the upper limit. For logarithmic axes, min and max are logs of the respective values. A variant which uses the nonlogarithmic number might be to use restrict expr to domain={\pgfmathrawx}{ min }{ max }. The non-starred versions also set unbounded coords=jump which leads to interrupted plots. tan(x) 5

/pgfplots/restrict expr to domain={ expression }{ min : max } /pgfplots/restrict expr to domain*={ expression }{ min : max } Appends an x coordinate lter which sets the x coordinate to -inf if the expression evaluates to something less than min and to inf if expression evaluates to something larger than max . The starred variant, restrict to domain* assigns min if expression is less then the lower limit and max if it is larger than the upper limit. The non-starred version also sets unbounded coords=jump which leads to interrupted plots. In contrast to restrict x to domain, expression can depend on anything which is valid during \addplot, in particular \coordindex or table columns (\thisrow{ column name } and friends). The expression doesnt need to depend on x at all. /pgfplots/@restrict to domain={ lter name }{ expression }{ min : max }0|1

A lowlevel (technical) key which allows to apply the restrict * to ... features also to something like hist/data. For example, @restrict to domain={hist/data}{}{0:1}{0} applies the domain-restriction to the histogram-input hist/data. The nal 0 means that it works in a similar way as the key restrict x to domain=0:1, i.e. it skips everything which is outside of [0, 1]. In a similar way, @restrict to domain={hist/data}{}{0:1}{1} applies the functionality of restrict x to domain*=0:1 to hist/data: it truncates values outside of [0, 1] to the domains end-points. The lter name is expected to be a coordinate name like x, y, z (or hist/data). The expression congures an expression which will be used rather than the value of lter name . It can be empty. The min : max are as described above. If the last argument is 1, any coordinate outside of the allowed domain will take the domain boundary as value. If it is 0, such a coordinate will get either inf or -inf.

/pgfplots/filter discard warning=true|false

You can nd somewhat more on coordinate ltering in Section 4.5.12: Interrupted Plots.

4.24

Transforming Coordinate Systems

Usually, pgfplots works with cartesian coordinates. However, one may want to provide coordinates in a dierent coordinate system. In this case, the data cs key can be used to identify the input coordinate system: /pgfplots/data cs=cart|polar|polarrad (initially cart)

Denes the coordinate system (cs) of the input coordinates. pgfplots will apply transformations if the argument does not match the expected coordinate system.

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CHAPTER 4. THE REFERENCE Use data cs if your input has a dierent coordinate system than the axis. More precisely, every axis type has its own coordinate system. For example, a normal axis has the cart coordinate system, whereas a polaraxis has a polar coordinate system. The use of data cs with a dierent argument than the default of your axis instructs pgfplots to apply transformations. At the time of this writing, pgfplots supports the following values for data cs: The data cs=cart denotes the cartesian coordinate system. It is the coordinate system of the usual axis (or its logarithmic variants). It can have three components, x, y , and z . Specifying it is only necessary if you have a non-cartesian axis: 120 150 90% Preamble: \pgfplotsset{width=7cm,compat=1.9}

210 240 300

330

270

The data cs=polar is the (twodimensional) coordinate system with (angle, radius), i.e. the rst component x is the angle and the second component y is the radius. The angle is a number in the periodic range [0, 360); the radius is any number. If a polar coordinate has a z component, it is taken as-is (the transformations ignore it). 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

At the point of this writing, the data cs method will work for most plot handlers. But for complicated plot handlers, further logic may be needed which is not yet available (for example, the quiver plot handler might not be able to convert its direction vectors correctly)61 . \pgfplotsaxistransformcs{ fromname }{ toname } Expects the current point in a set of keys, provided in the coordinate system fromname and replaces them by the same coordinates represented in toname . On input, the coordinates are stored in /data point/x, /data point/y, and /data point/z (the latter may be empty). The macro will test if there is a declared coordinate transformation from fromname to toname and invoke it. If there is none, it will attempt to convert to cart rst and then from cart to toname . If that does not exist either, the operation fails. \pgfplotsdefinecstransform{ fromname }{ toname }{ code } Denes a new coordinate system transformation. The code is expected to get input and write output as described for \pgfplotsaxistransformcs. Implementing a new coordinate system immediately raises the question in which math mode the operations shall be applied. pgfplots supports dierent socalled coordinate math systems for generic operations, and for each individual coordinate as well. These coordinate math systems can either use basic pgf math arithmetics, the fpu, or perhaps there will come a LuaTEX library. The documentation of this system is beyond the scope of this manual62 . Please consider reading the source-code comments and the source of existing transformations if you intend to write own transformations.61 In 62 Which

case you run into problems, consider writing a bug report or ask others in TEX online discussion forums. is quite comprehensive even without API documentation, as you will certainly agree...

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CHAPTER 4. THE REFERENCE

4.24.1

Interaction of Transformations

There are a couple of coordinate mappings in pgfplots. For each encountered coordinate in a coordinate stream (\addplot), it applies the following steps: 1. Remember the raw coordinates in math constants rawx, rawy, rawz, 2. Apply pre filter, 3. Apply x coord trafo, logarithm if necessary, and x filter (in this order), 4. Apply y coord trafo, logarithm if necessary, and y filter, 5. Apply z coord trafo, logarithm if necessary, and z filter, 6. Apply filter point, 7. Transfrom from data cs to the coordinate system of axis type, 8. Handle coordinate stacking (stack plots=x and/or stack plots=y). Here, pre filter takes no arguments; it simply prepares the following lters. Consequently, the rst item which actually accepts the input argument is x coord trafo. This method is part of the parsing; it accepts the raw coordinate which may be in symbolic form. The output of x coord trafo and its variants is a number. This number can be ltered or transformed by means of x filter and its variants. Note that x filter simply takes one argument: the result of x coord trafo. The intented meaning of x coord trafo is to dene how the raw string form as provided by the user makes its way into pgfplots. It is also the only transformation which has an inverse, the key x coord inv trafo. The inverse can be used to transform back from internal numeric form to some string for the end user. The key x coord trafo can only be dened as option to an axis, i.e. it it cannot be provided to \addplot. The meaning of x filter and its variants is to transform numbers or to conditionally throw away numbers (and thus the entire coordinate). Each \addplot can receive its own (set of) lters. The key filter point accepts all arguments (more precisely: the result of the preceding steps). It can rely on x, y , and z , and it can change any of them. The way it accepts the coordinates is by means of keys /data point/x and its variants for y and z . In principle, filter point is the most general lter. However, you can dene both x filter and filter point, and both will be applied. Each \addplot can receive its own filter point. The implementation for the key data cs is similar to filter point in that it accepts the result of all previous mapping steps. However, it maps from a welldened input coordinate system to some welldened internal coordinate system (which is inherent to the axis). Each \addplot can receive its own data cs. Finally, stack plots takes measures to add/subtract the results. Stacking of plots is a property of the axis; it is not intented to be provided as argument to \addplot63 .

4.25

Fitting Lines Regression

This section documents the attempts of pgfplots to t lines to input coordinates. pgfplots currently supports create col/linear regression applied to columns of input tables. The feature relies on PgfplotsTable, it is actually implemented as a table postprocessing method. /pgfplots/table/create col/linear regression={ key-value-cong } A style for use in \addplot table which computes a linear (least squares) regression y (x) = a x + b using the sample data (xi , yi ) which has to be specied inside of key-value-cong (see below). It creates a new column on-the-y which contains the values y (xi ) = a xi + b. The values a and b will be stored (globally) into \pgfplotstableregressiona and \pgfplotstableregressionb.63 Also

The example above has two plots: one showing the data and one containing the linear regression line. We use y={create col/linear regression={}} here, which means to create a new column64 containing the regression values automatically. As arguments, we need to provide the y column name explicitly65 . The x value is determined from context: linear regression is evaluated inside of \addplot table, so it uses the same x as \addplot table (i.e. if you write \addplot table[x={ col name }], the regression will also use col name as its x input). Furthermore, it shows the line parameters a and b in the legend. Note that the uncommented line with \xdef\slope{\pgfplotstableregressiona} is useful if you have more than one regression line: it copies the value of \pgfplotstableregressiona (in this case) into a new global variable called \slope. This allows to use \slope instead of \pgfplotstableregressiona even after \pgfplotstableregressiona has been overwritten. The following key-value-cong keys are accepted as commaseparated list: /pgfplots/table/create col/linear regression/table={ \macro or le name } (initially empty) Provides the table from where to load the x and y columns. It defaults to the currently processed one, i.e. to the value of \pgfplotstablename.

64 The y={create col/ feature is available for any other PgfplotsTable postprocessing style, see the create on use documentation in the PgfplotsTable manual. 65 In fact, pgfplots sees that there are only two columns and uses the second by default. But you need to provide it if there are at least 3 columns.

Provides the source of xi and yi data, respectively. The argument column is usually a column name of the input table, yet it can also contain [index] integer to designate column indices (starting with 0), create on use specications or aliases (see the PgfplotsTable manual for details on create on use and alias). The initial conguration (an empty value) checks the context where the linear regression is evaluated. If it is evaluated inside of \pgfplotstabletypeset, it uses the rst and second table columns. If it is evaluated inside of \addplot table, it uses the same x input as the \addplot table statement. The y key needs to be provided explicitly (unless the table has only two columns). /pgfplots/table/create col/linear regression/xmode=auto|linear|log /pgfplots/table/create col/linear regression/ymode=auto|linear|log (initially auto) (initially auto)

Enables or disables processing of logarithmic coordinates. Logarithmic processing means to apply ln before computing the regression line and exp afterwards. The choice auto checks if the column is evaluated inside of a pgfplots axis. If so, it uses the axis scaling of the embedding axis. Otherwise, it uses linear. In case of logarithmic coordinates, the log basis x and log basis y keys determine the basis.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Both keys allow to provide uncertainties (variances) to single data points. A high (relative) variance indicates an unreliable data point, a value of 1 is standard. The variance list key allows to provide variances directly as commaseparated list, for example variance list={1000,1000,500,200,1,1}. The variance key allows to load values from a table column name . Such a column name is (initially, see below) loaded from the same table where data points have been found. The column name may also be a create on use name.

If both, variance list and variance are given, the rst one will be preferred. Note that it is not necessary to provide variances for every data point. /pgfplots/table/create col/linear regression/variance src={ \table or le name } (initially empty) Allows to load the variance from another table. The initial setting is empty. It is acceptable if the variance column in the external table has fewer entries than expected, in this case, only the rst ones will be used. Limitations: Currently, pgfplots supports only linear regression, and it only supports regression together with \addplot table. Furthermore, long input tables might need quite some time.

4.26

Miscellaneous Options(initially false, default true)

/pgfplots/disablelogfilter=true|false

Disables numerical evaluation of log(x) in TEX. If you specify this option, any plot coordinates and tick positions must be provided as log(x) instead of x. This may be faster and possibly more accurate than the numerical log. The current implementation of log(x) normalizes x to m 10e and computes log(x) = log(m) + e log(10) where y = log(m) is computed with a Newton method applied to exp(y ) m. The normalization involves string parsing without TEX-registers. You can safely evaluate log(1 107 ) although TEX-registers would produce an underow for such small numbers.

/pgfplots/disabledatascaling=true|false

(initially false, default true)

Disables internal re-scaling of input data. Normally, every input data like plot coordinates, tick positions or whatever, are parsed without using TEXs limited number precision. Then, a transformation like T (x) = 10qm x a is applied to every input coordinate/position where m is the order of x base 10. Example: x = 1234 = 1.234 103 has order m = 4 while x = 0.001234 = 1.234 103 has order m = 2. The parameter q is the order of the axis width/height.

The eect of the transformation is that your plot coordinates can be of arbitrary magnitude like 0.0000001 and 0.0000004. For these two coordinates, pgfplots will use 100pt and 400pt internally. The transformation is quite fast since it relies only on period shifts. This scaling allows precision beyond TEXs capabilities.

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CHAPTER 4. THE REFERENCE The option disabledatascaling disables this data transformation. This has two consequences: rst, coordinate expressions like ( axis cs:x,y ) have the same eect as ( x,y ), no re-scaling is applied. Second, coordinates are restricted to what TEX can handle66 . So far, the data scale transformation applies only to normal axes (logarithmic scales do not need it).

/pgfplots/execute at begin plot={ commands } This axis option allows to invoke commands at the beginning of each \addplot command. The argument commands can be any TEX content. You may use this in conjunction with x filter=... to reset any counters or whatever. An example would be to change every 4th coordinate. /pgfplots/execute at end plot={ commands } This axis option allows to invoke commands commands can be any TEX content. /pgfplots/execute at begin axis={ commands } Allows to invoke commands at the end of \begin{axis} (or the other begin axis statements). The statement is execute as (almost) last statement before the preparation has been completed. /pgfplots/execute at end axis={ commands } The counterpart for execute at begin axis. The hook is actually superuos, it is executed immediately after before end axis. It is executed in the same TEX group as execute at begin axis. /pgfplots/execute at begin plot visualization={ commands } Allows to add customized code which is executed at the beginning of each plot visualization. In contrast to execute at begin plot, this happens not immediately during \addplot, but late during the postprocessing of \end{axis} when actual drawing commands are generated. One possible application is shown below: suppose you want to use \usepackage{ocg} in order to switch layers dynamically, for example in a beamer package. This can be implemented as follows: Dynamic PDF Layer Support (see Acrobat Layers) after each \addplot command. The argument

10 5 0 0 0.2 0.4 0.6 0.8 0.5 11 0

note that the axis scaling requires to compute 1/(xmax xmin ). The option disabledatascaling may lead to overow or underow in this context, so use it with care! Normally, the data scale transformation avoids this problem.

The execute * hooks insert the ocg-statements at the correct positions, and the single plot commands are added to dierent dynamic layers. Use the Acrobat Reader and its Layers Tab to switch each of them on or o. Note that it would not be enough to add the \begin{ocg}... statements right into the text since pgfplots postpones drawing commands until \end{axis} (splitting of survey and visualization phase). See http://www.texample.net/weblog/2008/nov/02/creating-pdf-layers for more details on ocg and how to obtain it. Technical note: these hooks are also inserted for \pgfplotsextra commands. /pgfplots/execute at end plot visualization={ commands } This is the counterpart of execute at begin plot visualization. /pgfplots/forget plot={ true,false } (initially false)

Allows to include plots which are not remembered for legend entries, which do not increase the number of plots and which are not considered for cycle lists. A forgotten plot can be some sort of decoration which has a separate style and does not inuence the axis state, although it is processed as any other plot. Provide this option to \addplot as in the following example. New Experiments (old in gray) e1 e2 e3% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 4. THE REFERENCE Since forgotten plots wont increase the plot index, they will use the same cycle list entry as following plots. The style every forget plot can be used to congure styles for each such plot: New Experiments (old in transparent) e1 e2 e3% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, the \addplot+ command means we are using the same cycle list as the following plot and forget plot style modies every forget style and yields transparency of the old experiments. Please note that every plot no index styles are not applicable here. A forgotten plot will be stacked normally if stack plots is enabled! /pgfplots/before end axis/.code={ ... } Allows to insert commands just before the axis is ended (see also execute at end axis). This option takes eect inside of the clipped area.% Preamble: \pgfplotsset{width=7cm,compat=1.9}

/pgfplots/after end axis/.code={ ... } Allows to insert commands right after the end of the clipped drawing commands. While before end axis has the same eect as if commands had been placed inside of your axis, after end axis allows to access axis coordinates without being clipped.

CHAPTER 4. THE REFERENCE Allows to communicate data to pgfplots which is essential to perform the visualization although pgfplots isnt aware of it. Suppose you want a scatter plot, which depends on the (x, y ) coordinates, the point meta data to draw individual colors and furthermore data which inuences the mark size. Thus, you need a total of 4 coordinates for every data point, although pgfplots supports only 3 in its initial conguration. Before we actually come to the main point of the problem, well talk about how to get a scatter plot which has individual colors and individual sizes. It is not sucient to set mark size alone, since mark size is evaluated only once, before markers are processed (the same holds for every mark). Thus, we can use scatter combined with scatter/@pre marker code/.append style={/tikz/mark size=\perpointmarksize}. The @pre marker code is installed for every marker of a scatter plot individually. Now, we come to the problem as such: where can we get the value for mark size, in our case called \perpointmarksize? A solution is visualization depends on (using the second input syntax at this point): 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we dene \perpointmarksize as 5*cos(deg(x)). The expression will be evaluated together with all other coordinates. Thus, everything which is available during the survey phase can be used here. This includes the nal coordinates x, y, z; the constant meta expands to the current per point meta data. Furthermore, \thisrow{ colname } expands to the value of a table column. The command visualization depends on evaluates and remembers every value in internal data structures. The remembered value is then available as \macro during the visualization phase. In our example, the @pre marker code is evaluated during the visualization phase and applies mark size=5*cos(deg(x)). The rst syntax, visualization depends on= \macro , tells pgfplots to use an already dened \macro . The second syntax with content \as \macro provides also the value. There can be more than one visualization depends on phrase. In case the stored value is not of numerical type67 , you can use the prex value before the argument, i.e. visualization depends on=value content \as \macro . /pgf/fpu={ true,false } visualization depends on=value \macro or

Such a value will be expanded and stored, but not parsed as number (at least not by pgfplots). (initially true)

This key activates or deactivates the oating point unit. If it is disabled (false), the core pgf math engine written by Mark Wibrow and Till Tantau will be used for plot expression. However, this engine has been written to produce graphics and is not suitable for scientic computing. It is limited to xed point numbers in the range 16384.00000. If the fpu is enabled (true, the initial conguration) the high-precision oating point library of pgf written by Christian Feuers anger will be used. It oers the full range of IEEE double precision computing in TEX. This FPU is also part of PgfplotsTable, and it is activated by default for create col/expr and all other predened mathematical methods.67 Or

if it is just a constant and youd like to improve speed.

4.27. TI KZ INTEROPERABILITY Use

\pgfkeys{/pgf/fpu=false}

341

in order to de-activate the extended precision. If you prefer using the fp (xed point) package, possibly combined with Mark Wibrows corresponding pgf library, the fpu will be deactivated automatically. Please note, however, that fp has a smaller data range (about 1017 ) and may be slower.

4.27

Tik Z Interoperability

pgfplots uses Tik Z/pgf as its backend layer. This implies that it inherits most of Tik Zs graphical features and adds a lot of own stu on top of it. However, the coordinate systems of Tik Z and pgfplots do not match up for good reason: pgfplots operates on logical (data) coordinates whereas Tik Z operates on image coordinates. Occasionally, one may want to synchronize both in order to generate a graphic. In this context, synchronize both means that they really use the same coordinate systems. This is far beyond the simple use-case of enrich a pgfplots picture by means of Tik Z annotations, compare Section 4.17. Consequently, this section addresses the question how to match the coordinates from Tik Z to pgfplots and viceversa. It explains how to match coordinates and it discusses the necessary conguration. There are a couple of keys in pgfplots which control the mapping of coordinates. The purpose of these keys is to implement visualization techniques, but they do things dierent than Tik Z (and they should). To match coordinates with Tik Z, one needs the following aspects: 1. Restrict your visualization type: a logarithmic axis simply may not t into Tik Z (to be more precise: it may t, but a Tik Z unit will correspond to a logunit in pgfplots). 2. Congure matching unit vectors by means of the x and y keys. The default conguration of Tik Z is to use x=1cm,y=1cm,z={(0,0)}. Note that these settings are usually overridden by pgfplots in order to respect width and height (and view for threedimensional axes). 3. Disable the data scaling by means of disabledatascaling: pgfplots will internally apply linear coordinate transformations in order to provide the data range required for oating point arithmetics (using approximately oating point precision). Disabling the data scaling means to restrict yourself to the (small) data range supported by Tik Zbut thats probably what you want in that case. 4. Dene anchor and position of the axis, probably using anchor=origin,at={(0,0)}. The at={(0,0)} congures pgfplots to place the axis at the Tik Z position (0,0) whereas anchor=origin means that pgfplots will place its data origin (0, 0, 0) at the place designated by at (see Section 4.19 for details). 5. Make sure that the pgfplots axis contains the data origin (0, 0, 0) in the displayed data range (i.e. congure xmin, xmax, ymin, and ymax appropriately). Without this, the anchor=origin key required in the previous item will be truncated to the next coordinate which is part of the displayed range. Here is a simple example, rst with Tik Z:\begin{tikzpicture} \coordinate (Point) at (1,2);

it displays a grid with x, y [1, 3] and shows a node inside of it. Now, we apply the keys discussed above to match this setting in pgfplots:

342 3 2 1 0 (-1,0) 1 1 (2,0) (1,2)

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% Preamble: \pgfplotsset{width=7cm,compat=1.9}

\begin{tikzpicture} \coordinate (Point) at (1,2); \begin{axis}[ % tell pgfplots to "grab" the axis at its % internal (0,0) coord: anchor=origin, % tell pgfplots to place its anchor at (0,0): % (This is actually the default and can % be omitted) at={(0pt,0pt)}, % tell pgfplots to use the "natural" dimensions: disabledatascaling, % tell pgfplots to use the same unit vectors % as tikz: x=1cm,y=1cm, % % this is just as usual in pgfplots. I guess % it is only useful if (0,0) is part of the % range... try it out. xmin=-1,xmax=3, ymin=-1,ymax=3,grid=both] % this uses the point defined OUTSIDE of the axis \draw [blue,fill] (Point) circle (2pt) node [right] {(1,2)}; % this uses a TIKZ coordinate (2,0) in the axis: \draw [blue,fill] (2,0) circle (2pt) node [right] {(2,0)}; % this here will always work inside of an axis: \draw [blue,fill] (axis cs:-1,0) circle (2pt) node [right] {(-1,0)}; \end{axis} \end{tikzpicture}

The example demonstrates several things: rst, it denes a coordinate in the enclosing tikzpicture and uses it inside of the axis (at the correct position). Second, it uses the standard Tik Z coordinate (2,0) inside of the axis, and it is placed at the expected position. Third, it uses the approach provided by pgfplots by using the axis cs to designate a coordinate (this last approach does also work without the coordinate matching). Here is an example which inserts a pgfplots graphics correctly into a tikzpicture: second

third rst

fourth

4.28. LAYERS% Preamble: \pgfplotsset{width=7cm,compat=1.9}

343

% requires \usepgfplotslibrary{patchplots} \begin{tikzpicture} \begin{axis}[ % tell pgfplots to "grab" the axis at its internal (0,0) coord: anchor=origin, % tell pgfplots to place its anchor at (0,0): % (This is actually the default and can be omitted) at={(0pt,0pt)}, % tell pgfplots to use the "natural" dimensions: disabledatascaling, % tell pgfplots to use the same unit vectors as tikz: x=1cm,y=1cm, % hide axis, ] \addplot[patch,patch type=coons, shader=interp,point meta=explicit] coordinates { (0,0) [0] % first corner (1,-1) [0] % bezier control point between (0) and (3) (4,0.7) [0] % bezier control point between (0) and (3) % (3,2) [1] % second corner (4,3.5) [1] % bezier control point between (3) and (6) (7,2) [1] % bezier control point between (3) and (6) % (7,1) [2] % third corner (6,0.6) [2] % bezier control point between (6) and (9) (4.5,-0.5) [2] % bezier control point between (6) and (9) % (5,-2) [3] % fourth corner (4,-2.5) [3] % bezier control point between (9) and (0) (-1,-2) [3] % bezier control point between (9) and (0) }; \end{axis} % this requires pgf 2.10 \begin{scope}[every node/.style={circle,inner sep=2pt,fill=black}] \node[pin=140:first] at (0,0) {}; \node[pin=second] at (3,2) {}; \node[pin=45:third] at (7,1) {}; \node[pin=0:fourth] at (5,-2) {}; \end{scope} \end{tikzpicture}

The example employs one of the patch plots of the patchplots library. Since these graphical elements typically require depth information (z buffering) and color data (point meta), they are only available inside of pgfplots. However, the conguration above ensures that coordinates match one-to-one between pgfplots and Tik Z. The hide axis ag disables anything of pgfplots, so only the visualized patch plot remains68 .

4.28

Layers

It is important that several parts of an axis are drawn on top of others. Usually, pgfplots ensures this by drawing them in a suitable sequence (usually background followed by grid lines, followed by tick lines and tick labels, followed by plots and nally axis descriptions). While this works reasonable in most cases, there are cases where more control is desired. One common use-case is if multiple axes shall be drawn into the same picture: here, the sequence from above should be applied to all involved axes simultaneously.

4.28.1

Summary

This section is the technical reference for using and customizing layered graphics in pgfplots. As such, it is hard reading. For most purposes, the following is completely sucient for you: If you want to enable layered graphics, put the following statement into the tikzpicture which is supposed to have layered graphics:68 Note

that the (0, 0, 0) coordinate of pgfplots is part of the data range here.

344\begin{tikzpicture} \pgfplotsset{set layers} \begin{axis} ... \end{axis} % perhaps a second axis which should use the same layers? \begin{axis} ... \end{axis} \end{tikzpicture}

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This enables layered graphics for that specic tikzpicture. You may want layered graphics if you have multiple axes in the same picture, of if you have specic needs for your plot. Consider reading on layer if you want to move particular elements of your axis to a dierent layer.

4.28.2

Using Predened Layers

The main key to control layered graphics with pgfplots is set layers: /pgfplots/set layers=none| layer conguration name (initially none)

This key enables layered graphics for either the current axis or for all following axes. Enabling layered graphics has the eect that the order in which graphical elements are given is unrelated to the ordering in which they will be drawn. The main benet is if you have multiple axes in the same gure: the axes can share the same layers. The invocation set layers=none disables layered graphics.

The invocation set layers (without equal sign and without arguments) is the same as if you would write set layers=default. In all other cases, set layers expects a layer conguration name . There are two predened congurations available (the prex /pgfplots/layers/ is optional): /pgfplots/layers/standard (no value)

A layer conguration which denes the layers axis background, axis grid, axis ticks, axis lines, axis tick labels, main, axis descriptions, axis foreground. They are drawn in the order of appearance. /pgfplots/layers/axis on top (no value)

A layer conguration which uses the same layer names as layers/standard, but with a dierent sequence: axis background, main, axis grid, axis ticks, axis lines, axis tick labels, axis descriptions, axis foreground. This layer is automatically used if the key axis on top is used together with set layers= any layer conguration name . As soon as the key set layers= layer conguration name is encountered, pgfplots starts the pgf command \pgfsetlayers{ layer names } with the layer names of the respective conguration. Usually, this replaces the current layer conguration of the embedding tikzpicture. Furthermore, set layers stores the name of layer conguration name such that every following axis knows how to map graphical elements to layer names. There is one huge dierence to any other key which tunes pgfplots: layer congurations are properties of a complete tikzpicture whereas any other option aects only axis objects and their contents. Layers, however, aect every graphical element of the embedding picture. Due to this property, layer congurations need to be given at one of several supported positions: 1. Directly within the picture:\begin{tikzpicture} \pgfplotsset{set layers=default} \begin{axis} ... \end{axis} \end{tikzpicture}

4.28. LAYERS

345

This option explicitly tells the reader of your source code that a signicant portion of your picture has been changed: the complete picture has and uses a layer conguration name (in this case default). 2. As option for one or more axes which is/are directly within the picture:\begin{tikzpicture} \begin{axis}[set layers] ... \end{axis} \end{tikzpicture}

Here, pgfplots implicitly communicates its layer conguration to the enclosing tikzpicture. Thus, the eect of set layers is not local to an axis ; it survives until \end{tikzpicture}. Any other option only survives until \end{axis}. In this case, only the last activated layer conguration will apply to the picture. Limitation: no environments or local TEX groups allowed. Standard usages as within the examples of this manual will always work. But since the layer name conguration is essentially part of a pgf picture (at a low level), one cannot arbitrarily set them; pgf will complain if they A are changed within some nested TEX groups or L TEX environments. Typically, you will never need to worry about this. In short, the following examples are forbidden because the axis is within locally nested groups.\begin{tikzpicture} {% FORBIDDEN! Consider using case (1) above! \begin{axis}[set layers] ... \end{axis} } \end{tikzpicture}

These examples are forbidden because the layer conguration will be cleared by the } of the rst forbidden example and by the \end{scope} of the second example. A solution would be one of the dierent placement options (i.e. choice (1.) or (3.)). 3. outside of any picture:\pgfplotsset{set layers=default} \begin{tikzpicture} \begin{axis} ... \end{axis} \end{tikzpicture}

This choice congures the layer conguration for every following tikzpicture. Limitation: axis alignment restricted to inner anchors. This applies only if you changed the default value of anchor (which is anchor=south west). Any axis which uses layered graphics should use one of the following values of anchor: north, north west, west, south west, south, south east, east, north east, north, center, origin, above origin, left of origin, right of origin, below origin. In case you really need another anchor, pgfplots requires the use of cell picture=true, causing the layers to be local for that specic axis. The technical background for this limitation is a hen-and-egg problem: outer anchors (like outer south west) are only available after the complete axis has been generated and layers can only be drawn after each drawing instruction has been issued. The technical keys for further reading are cell picture=false or cell picture=if necessary (one of them is active for layered graphics).

346 \pgfplotssetlayers

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An alias for \pgfplotsset{set layers}. It activates the layers/default layer conguration. \pgfplotssetlayers{ layer conguration name } An alias for \pgfplotsset{set layers={ layer conguration name }}. Key handler key /.define layer set={ ordered layer names }{ style denitions } Allows to dene a new layer set conguration named key . Afterwards, key is a valid argument for set layers= key . The rst argument ordered layer names is a comma-separated list of layer names. The names are arbitrary, and \pgfdeclarelayer will be called for every encountered argument69 . There is just one magic name: the layer main should be part of every ordered layer names as it will contain every graphical element which is not associated with a specic layer. The second argument style denitions contains options just as if you would have written key /.style={ style denitions }. The style denitions are supposed to contain pgfplots style redenitions which make use of each encountered element of ordered layer names . This is probably best explained by an example: the layers/standard layer conguration is dened by\pgfplotsset{ layers/standard/.define layer set= {axis background,axis grid,axis ticks,axis lines,axis tick labels,main,% axis descriptions,axis foreground} { grid style= {/pgfplots/on layer=axis grid}, tick style= {/pgfplots/on layer=axis ticks}, axis line style= {/pgfplots/on layer=axis lines}, label style= {/pgfplots/on layer=axis descriptions}, legend style= {/pgfplots/on layer=axis descriptions}, title style= {/pgfplots/on layer=axis descriptions}, colorbar style= {/pgfplots/on layer=axis descriptions}, ticklabel style= {/pgfplots/on layer=axis tick labels}, axis background@ style={/pgfplots/on layer=axis background}, 3d box foreground style={/pgfplots/on layer=axis foreground}, }, }

This denition declares a couple of layers, and it adjusts pgfplots styles by adding on layer commands. The arguments for on layer are the elements of ordered layer names . Note that if you have an element in ordered layer names which is never referenced inside of style denitions , this layer will always be empty. In other words: the only reference to the names in ordered layer names is style denitions , pgfplots has no hard-coded magic layer names (except for main as explained above). Since the second argument style denitions denes key to be a normal style key, one can simply use key in order to set style denitions . This allows to inherit them. For example, the layers/axis on top layer conguration is dened by means of\pgfplotsset{ /pgfplots/layers/axis on top/.define layer set= {axis background,main,axis grid,axis ticks,axis lines,axis tick labels,% axis descriptions,axis foreground} {/pgfplots/layers/standard} }

i.e. it only redenes the sequence of the layers and re-uses the style denitions of layers/standard. Any number of layer congurations can be dened.

4.28.3

Changing the Layer of Graphical Elements

There are a couple of keys which change the layer of a graphical element. /pgfplots/on layer={ layer name } Providing this key somewhere in a pgfplots style or inside of a pgfplots axis will change the layer for all graphical elements for which the style applies.69 To

be more precise: set layers calls \pgfdeclarelayer when it uses ordered layer names .

4.29. TECHNICAL INTERNALS For example,

will change the layer for any grid lines to axis foreground. The argument layer name is expected to be part of the current layer conguration, i.e. the argument of set layers should contain it. Note that if you have two plots with dierent values of on layer, you may also want to enable clip mode=clip individual or to deactivate clipping altogether using clip=false. Clipping options need to be provided as option to the axis, not to the plot. The technical background is that clip paths needs to be replicated for the layer on which the drawing is supposed to happen otherwise they will be applied to the wrong layer. /pgfplots/mark layer=auto|like plot| layer name (initially auto)

An advanced key which denes the layer for plot marks. It is typically the best choice to leave it at auto. If you write \addplot[on layer= layer name ], the layer will be used for the complete plot. Plot marks are treated with special care, so you can dene an own layer for plot marks. The initial choice auto will automatically dene a suitable choice, leaving the responsability with pgfplots. Here, suitable means to respect clip mode and clip marker paths in a way such that plot marks will not be clipped even though the default layer for your plot will be clipped. The choice like plot will pack the marks onto the same layer as the plot they belong to. This might cause clipped markers, i.e. markers which are only displayed partially if they are close to the boundary of the axis. Finally, one can provide any layer name , just as for on layer but the layer can be dierent from the layer used for the plot.

4.29

Technical Internals

This section describes keys which are usually set by internal routines it is typically unnecessary to use them. However, they may impose limitations or inuence performance. Such cases are documented clearly in other sections of this manual. This here is the reference on the involved internals. /pgfplots/cell picture=true|false|if necessary (initially true)

This key is set automatically by pgfplots if necessary (for example by set layers).

Typically, pgfplots creates a so-called cell picture. A cell picture is a separate picture which is typeset into a node. Finally, the node is shifted to fulll special anchor requirements. The necessity for a cell picture is given if the anchor of an axis is only known after the complete axis has been drawn. The initial choice true means that pgfplots will create a cell picture for every axis. This allows all anchors, but it is unsuited if multiple graphics layers are desired or if one wants SVG export. In order to create a cell picture, pgfplots interrupts the embedding tikzpicture, draws a new tikzpicture, and nally typesets the result into a node. The choice false tells pgfplots to draw its paths directly into the embedding tikzpicture. Such an approach is necessary if the axis shall use layers of the embedding tikzpicture. This is possible if and only if the anchor can be determined without actually drawing the complete axis. If so, pgfplots will modify the transformation matrix in advance. Note that axes with cell picture=false will contain all the usual anchors the only dierence is that the axis itsself can only use one of the following anchors for its alignment: north, north west, west, south west, south, south east, east, north east, north, center, origin, above origin, left of origin, right of origin, below origin. The choice if necessary will check if the chosen anchor is one of the list above. If so, it will use cell picture=false. Otherwise, it will use cell picture=true. /pgfplots/compat/show suggested version=true|false (initially true)

If enabled, pgfplots will show you which value for compat= version results in the largest active feature set and highest quality.

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CHAPTER 4. THE REFERENCE This key will generate a warning if the current version is so old that the quality degrades seriously. The notication will be printed to your .log le (during \end{document}).

Chapter 5

Related LibrariesThis section describes some libraries which come with pgfplots, but they are more or less special and need to be activated separately.

5.1

Clickable Plots

A \usepgfplotslibrary{clickable} % L TEX and plain TEX \usepgfplotslibrary[clickable] % ConTEXt A \usetikzlibrary{pgfplots.clickable} % L TEX and plain TEX \usetikzlibrary[pgfplots.clickable] % ConTEXt A library which generates small popups whenever one clicks into a plot. The popup displays the coordinate under the mouse pointer, supporting the optional snaptonearest clickable coords feature with customizable displayed information. Furthermore, the library allows to display slopes if one holds the mouse pressed and drags it to another point in the plot.

The library has two purposes: to compute slopes in a simple way1 and to provide related, optional information to single data points which are not important enough to be listed in the main text (like prototype parameters or other technical things).

5.1.1

Overview

It is completely sucient to write

\usepgfplotslibrary{clickable}

in the document preamble. This will automatically prepare every plot. The library works with Acrobat Javascript and pdf forms: every plot becomes a pushbutton.

These screenshots show the result of clicking into the axis range (left column) and of dragging from one point to another (right column). The second case shows the result of Drag-and-Drop: it displays start- and1 The

author is applied mathematician...

349

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CHAPTER 5. RELATED LIBRARIES

end points and the equation for the line segment between between the rst point of the drag- and drop and the second point where the mouse has been released. The line segment is where m = (y1 y0 )/(x1 x0 ) is the slope and n the oset chosen such that l(x0 ; . . . ) = y0 . For logarithmic plots, logarithms will be applied before computing slopes. l(x; x0 , y0 , x1 , y1 ) = m x + n

These screen shots show the result of drag- and drop for logarithmic axes: the end points show, again, the coordinates (without logs) and the form eld in the middle shows the slope and oset of the linear equation in log coordinates. The log basis for any logarithmic axes is usually 10, but it respects the current setting of log basis x and log basis y. The applied log will always use the same logarithm which is also used for the axis descriptions (this is not necessarily the same as used by PgfplotsTable!). This document has been produced with the clickable library, so it is possible to load it into Acrobat Reader and simply click into a plot. /pgfplots/clickable coords={ displayed text } Activates a snaptonearest feature when clicking onto plot coordinates. The displayed text is the coordinates x and y value by default (i.e. you write just clickable coords without an equal sign).% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Now, clicking onto a data point yields Level 7 (q=40) whereas clicking besides a data point results in the click coordinates as before,

5.1. CLICKABLE PLOTS Note that logarithmic slopes work as before.

351

If you want the (x, y ) values to be displayed, use the special placeholder string (xy) inside of displayed text . As an example, we consider again the scatter/classes example of page 100:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we nd popups like

. The displayed text is a richtext string displayed with Javascript. For most purposes, it is used like an unformatted C string: it contains characters, perhaps line breaks with \n or tabulators with \t, but it should not contain TEX formatting instructions, especially no math mode (the (xy) replacement text is formatted with sprintf, see below). Consider clickable coords code in case youd like to preprocess data before displaying it. If you experience problems with special characters, try prepending a backslash to them. If that doesnt work either, try to prex the word with \\ and/or with \string. Consider using clickable coords size if you intend to work with multiline elds and the size allocation needs improvements. In fact, displayed text can even contain richtext (=XHTML) formatting instructions like <br/> (note the nal slash) or <span style="color:\#7E0000;">text</span> (note the backslash before #) which changes the color for text. The <span style=""> arguments are CSS elds, consider an HTML reference for a list of CSS attributes. It is possible to use clickable coords together with three dimensional axes. Note that dynamic (clickable) features of a three dimensional axis without clickable coords will be disabled (they appear to be useless). Furthermore, three dimensional axes do not support slope calculations; only the snap tonearest feature is available. Consider using annot/snap dist=6 to increase the snaptonearest distance. The clickable coords can be specied for all plots in an axis (as in the examples above), but also once for every single \addplot commands for which the snaptonearest feature is desired (with dierent displayed text ). If multiple clickable coords are on the same position, each click chooses the next one (in the order of appearance). /pgfplots/clickable coords code={ TEX code which denes \pgfplotsretval } A variant of clickable coords which allows to prepare the displayed information before it is handed over to Javascript.

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CHAPTER 5. RELATED LIBRARIES The value should be TEX code which denes \pgfplotsretval somehow. The result is used as simple, unformatted string which is associated to coordinates. Consider using \pgfmathprintnumberto[verbatim]{ number }\macroname \edef\pgfplotsretval{Number=\macroname} to provide number printing. The \pgfmathprintnumberto[verbatim] doesnt use math mode to format a number2 , and it writes its result into \macroname. The name \macroname is arbitrary, use anything like \eps or \info. The \edef means expanded denition and has the eect of expanding all macros to determine the value, in our case Number= the value . The following example uses it twice to prettyprint the data:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

resulting in . The TEX code is evaluated inside of a local scope, all locally declared variables are freed afterwards (thats why you can use any names you want). /pgfplots/clickable coords size=auto or { max chars } or { max chars x,max chars y } auto) This is actually just another name for annot/popup size snap, see its documentation below. (initially

5.1.2

Requirements for the Library

A The library relies on the L TEX packages insdljs (Insert document level Javascript) and eforms which are both part of the freely available AcroTeX education bundle [4]3 . The insdljs package creates a temporary le with extension .djs.

At the time of this writing, only Adobe Acrobat Reader interpretes Javascript and Forms properly. The library doesnt have any eect if the resulting document is used in other viewers (as far as I know).

Note that although this library has been written for pgfplots, it can be used independently of a pgfplots environment.2 See 3 These

the PgfplotsTable manual for details about number printing. A A packages rely on L TEX, so the library is only available for L TEX, not for plain TEX or ConTEXt.

5.1. CLICKABLE PLOTS

353

Compatibility issues: There a several restrictions when using this library. Most of them will vanish in future versions but up to now, I cant do magic. The library does not yet support rotated axes. Use clickable=false for those axes. The library works only with pdflatex; dvips or dvipdfm are not supported4 . Up to now, it is not possible to use this library together with the external library and other image externalization methods of Section 7.

To be more precise, you can (with two extra preamble lines, see below) get correctly annotated, exported pdf documents, but the \includegraphics command does not import the dynamic features. In case you decide to use this workaround, you need to insert% \maxdeadcycles=10000 % in case you get the error Output loop---<N> consecutive dead cycles. \usepackage[pdftex]{eforms}

before loading pgf, Tik Z or pgfplots. The \maxdeadcycles appears to be necessary for large documents, try it out. As long as you are working on a draft version of your document, you might want to use\pgfkeys{/pgf/images/include external/.code={\href{file:#1}{\pgfimage{#1}}}}

in your preamble. This will generate hyperlinks around the graphics les which link to the exported gures. Clicking on the hyperlinks opens the exported gure which, in turn, has been generated with the clickable library and allows dynamic features5 . The library automatically calls \begin{Form} at \begin{document} and \end{Form} at the end of the document. This environment of hyperref is necessary for dynamic user interaction and should be kept in mind if the document contains other form elements.

Acknowledgements: I have used a Javascript sprintf implementation of Kevin van Zonneveld [6] (the Javascript API has only a limited set of conversions).

5.1.3

Customization

It is possible to customize the library with several options. /pgfplots/clickable=true|false (initially true)

Allows to disable the library for single plots. (initially ["RGB",1,1,.855])

Possible choices are transparent, gray, RGB or CMYK color specied as fourelementarrays of the form ["RGB", red , green , blue ]. Each color component is between 0 and 1. Again: this option is for Javascript. It is not possible to use colors as in pgf. /pgfplots/annot/point format={ sprintf-format } /pgfplots/annot/point format 3d={ sprintf-format } (initially (%.1f,%.1f)) (initially (%.1f,%.1f,%.1f))

Allows to provide an sprintf format string which is used to ll the annotations with text. The rst argument to sprintf is the x-coordinate and the second argument is the y -coordinate. The point format 3d variant is used for any threedimensional axis whereas the point format is used (only) for twodimensional ones. The every semilogx axis, every semilogy axis and every loglog axis styles have been updated tofact, they should be. I dont really know why they dont . . . any hint is welcome. special treatment needs the external les in the same base directory as the main document, so this approach is most certainly not suitable for a nal document.5 This 4 In

such that every logarithmic coordinate is displayed in scientic format. /pgfplots/annot/slope format={ sprintf-format } (initially %.1f*x %+.1f) Allows to provide an sprintf format string which is used to ll the slopeannotation with text. The rst argument is the slope and the second the line oset. /pgfplots/annot/printable=true|false (initially false) Allows to congure whether the small annotations will be printed. Otherwise, they are only available on screen. (initially font.Times) Allows to choose a Javascript font for the annotations. Possible choices are limited to what Javascript A accepts (which is not the same as L TEX). The default fonts and its names are shown below. Font Name Times-Roman Times-Bold Times-Italic Times-BoldItalic Helvetica Helvetica-Bold Helvetica-Oblique Helvetica-BoldOblique Courier Courier-Bold Courier-Oblique Courier-BoldOblique Symbol ZapfDingbats /pgfplots/annot/textSize={ Size in Point } Sets the text size of annotations in points. /pgfplots/annot/popup size generic=auto or { x } or { x,y } /pgfplots/annot/popup size snap=auto or { x } or { x,y } /pgfplots/annot/popup size={ value } (initially auto) (initially auto) Name in Javascript font.Times font.TimesB font.TimesI font.TimesBI font.Helv font.HelvB font.HelvI font.HelvBI font.Cour font.CourB font.CourI font.CourBI font.Symbol font.ZapfD (initially 11)

/pgfplots/annot/font={ Javascript font name }

The rst key denes the size of popups if you just click into an axis. The second key denes the size of popups for the snaptonearest feature (i.e. those prepared by clickable coords). The third key sets both to the same value . The argument can be auto in which case pgfplots tries to be smart and counts characters. This may fail for multiline texts. The choice x provides the horizontal size only, in units of annot/textSize. Thus, annot/popup size generic=6 makes the popup 6 11 points wide. In this case, only one line will be allocated. Finally, x,y allows to provide horizontal and vertical size, both in units of annot/textSize. See also clickable coords size which is an alias for annot/popup size snap. /pgfplots/annot/snap dist={ Size in Point } (initially 4) Denes the size within two mouse clicks are considered to be equivalent, meased in points (Euclidean distance). /pgfplots/annot/richtext=true|false (initially true) Enables or disables richtext formatting in clickable coords arguments. Richtext is kind of XHTML and allows CSS styles like colors, font changes and other CSS attributes, see the documentation for clickable coords for details. The case annot/richtext=false is probably more robust.

5.2. COLORMAPS

355

5.1.4

Using the Clickable Library in Other Contexts

This library provides essentially one command, \pgfplotsclickablecreate which creates a clickable area of predened size, combined with Javascript interaction code. It can be used independently of pgfplots. \pgfplotsclickablecreate[ required key-value-options ] Creates an area which is clickable. A click produces a popup which contains information about the point under the cursor. The complete (!) context needs to be provided using key-value-pairs, either set before calling this method of inside of [ required key-value-options ]. This command actually creates an AcroForm which invokes Javascript whenever it is clicked. A Javascript Object is created which represents the context (axis limits and options). This Javascript object is available at runtime. This method is public and it is not restricted to pgfplots. The pgfplots hook simply initializes the required key-value-pairs. This method does not draw anything. It initializes only a clickable area and Javascript code. The required key-value-pairs are documented below. Attention: Complete key-value validation is not performed here. It can happen that invalid options will produce Javascript bugs when opened with Acrobat Reader. Use the Javascript console to nd them. All options described in the following are only interesting for users who intend to use this library without pgfplots. /pgfplots/annot/width={ dimension } (initially -)

This required key communicates the areas width to \pgfplotsclickablecreate. It must be a TEX dimension like 5cm. /pgfplots/annot/height={ dimension } (initially -)

This required key communicates the areas height to \pgfplotsclickablecreate. It must be a TEX dimension like 5cm. /pgfplots/annot/jsname={ string } (initially -)

This required key communicates a unique identier to \pgfplotsclickablecreate. This identier is used to identify the object in Javascript, so there cant be more than one of them. If it is empty, a default identier will be generated. /pgfplots/annot/xmin={ /pgfplots/annot/xmax={ /pgfplots/annot/ymin={ /pgfplots/annot/ymax={ number number number number } } } }

(initially empty)

These required keys communicate the axis limits to \pgfplotsclickablecreate. They should be set to numbers which can be assigned to a Javascript oating point number (standard IEEE double precision). /pgfplots/annot/collected plots={ nested arrays } (initially empty)

The low level interface to implement a snaptonearest feature. The value is an array of plots, where each plot is again an array of coordinates and each coordinate is an array of three elements, x, y and text. Please consult the code comments for details and examples.

5.2

Colormaps

An extension by Patrick H acker

CHAPTER 5. RELATED LIBRARIES

\usetikzlibrary[pgfplots.colormaps] % ConTEXt A small library providing a number of additional colormaps. Many of these colormaps originate from the free Matlab package SC powerful image rendering of Oliver Woodford. The purpose of this library is to provide further colormaps to all users and to provide some of them which are similar to those used by Matlab (). /pgfplots/colormap/autumn A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={autumn}{rgb255=(255,0,0) rgb255=(255,255,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/bled A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={bled}{rgb255=(0,0,0) rgb255=(43,43,0) rgb255=(0,85,0) rgb255=(0,128,128) rgb255=(0,0,170) rgb255=(213,0,213) rgb255=(255,0,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/bright A style which is equivalent to (style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/bone A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={bone}{[1cm]rgb255(0cm)=(0,0,0) rgb255(3cm)=(84,84,116) rgb255(6cm)=(167,199,199) rgb255(8cm)=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/cold A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={cold}{rgb255=(0,0,0) rgb255=(0,0,255) rgb255=(0,255,255) rgb255=(255,255,255)} }

(style, no value)

5.2. COLORMAPS

357

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/copper A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={copper}{[1cm]rgb255(0cm)=(0,0,0) rgb255(4cm)=(255,159,101) rgb255(5cm)=(255,199,127)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/copper2 A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={copper2}{rgb255=(0,0,0) rgb255=(68,62,63) rgb255=(170,112,95) rgb255=(207,194,138) rgb255=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/earth A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={earth}{rgb255=(0,0,0) rgb255=(0,28,15) rgb255=(42,39,6) rgb255=(28,73,33) rgb255=(67,85,24) rgb255=(68,112,46) rgb255=(81,129,83) rgb255=(124,137,87) rgb255=(153,147,122) rgb255=(145,173,164) rgb255=(144,202,180) rgb255=(171,220,177) rgb255=(218,229,168) rgb255=(255,235,199) rgb255=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/gray A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={gray}{rgb255=(0,0,0) rgb255=(255,255,255)} }

(style, no value)

This colormap is an alias for the standard colormap/blackwhite. This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/hot2 A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={hot2}{[1cm]rgb255(0cm)=(0,0,0) rgb255(3cm)=(255,0,0) rgb255(6cm)=(255,255,0) rgb255(8cm)=(255,255,255)} }

(style, no value)

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CHAPTER 5. RELATED LIBRARIES

Note that this particular choice ships directly with pgfplots, you do not need to load the colormaps library for this value. This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/hsv A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={hsv}{rgb255=(255,0,0) rgb255=(255,255,0) rgb255=(0,255,0) rgb255=(0,255,255) rgb255=(0,0,255) rgb255=(255,0,255) rgb255=(255,0,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/hsv2 A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={hsv2}{rgb255=(0,0,0) rgb255=(128,0,128) rgb255=(0,0,230) rgb255=(0,255,255) rgb255=(0,255,0) rgb255=(255,255,0) rgb255=(255,0,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/jet A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={jet}{rgb255(0cm)=(0,0,128) rgb255(1cm)=(0,0,255) rgb255(3cm)=(0,255,255) rgb255(5cm)=(255,255,0) rgb255(7cm)=(255,0,0) rgb255(8cm)=(128,0,0)} }

(style, no value)

Note that this particular choice ships directly with pgfplots, you do not need to load the colormaps library for this value. This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/pastel A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={pastel}{rgb255=(0,0,0) rgb255=(120,0,5) rgb255=(0,91,172) rgb255=(215,35,217) rgb255=(120,172,78) rgb255=(255,176,24) rgb255=(230,255,0) rgb255=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name.

359 (style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/sepia A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={sepia}{rgb255(0cm)=(0,0,0) rgb255(1cm)=(26,13,0) rgb255(18cm)=(255,230,204) rgb255(20cm)=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/spring A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={spring}{rgb255=(255,0,255) rgb255=(255,255,0)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/summer A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={summer}{rgb255=(0,128,102) rgb255=(255,255,102)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/temp A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={temp}{rgb255=(36,0,217) rgb255=(25,29,247) rgb255=(41,87,255) rgb255=(61,135,255) rgb255=(87,176,255) rgb255=(117,211,255) rgb255=(153,235,255) rgb255=(189,249,255) rgb255=(235,255,255) rgb255=(255,255,235) rgb255=(255,242,189) rgb255=(255,214,153) rgb255=(255,172,117) rgb255=(255,120,87) rgb255=(255,61,61) rgb255=(247,40,54) rgb255=(217,22,48) rgb255=(166,0,33)} }

(style, no value)

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CHAPTER 5. RELATED LIBRARIES This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/thermal A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={thermal}{rgb255=(0,0,0) rgb255=(77,0,179) rgb255=(255,51,0) rgb255=(255,255,0) rgb255=(255,255,255)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name. /pgfplots/colormap/winter A style which is equivalent to\pgfplotsset{ /pgfplots/colormap={winter}{rgb255=(0,0,255) rgb255=(0,255,128)} }

(style, no value)

This colormap is similar to one shipped with Matlab () under a similar name.

5.3

Dates as Input Coordinates

A \usepgfplotslibrary{dateplot} % L TEX and plain TEX \usepgfplotslibrary[dateplot] % ConTEXt A \usetikzlibrary{pgfplots.dateplot} % L TEX and plain TEX \usetikzlibrary[pgfplots.dateplot] % ConTEXt A library which allows to use dates like 2008-01-01 or dates with time like 2008-01-01 11:35 as input coordinates in plots. The library converts dates to numbers and tick labels will be pretty-printed dates (or times).

This library is documented in Section 4.22.2 on page 323.

5.4

Image Externalization

A \usepgfplotslibrary{external} % L TEX and plain TEX \usepgfplotslibrary[external] % ConTEXt A \usetikzlibrary{pgfplots.external} % L TEX and plain TEX \usetikzlibrary[pgfplots.external] % ConTEXt The external library oers a convenient method to export every single tikzpicture into a sepaA rate .pdf (or .eps). Later runs of L TEX will simply include these graphics, thereby reducing typesetting time considerably.

This library is documented in more detail in Section 7.1 Export to pdf/eps. The external library has been written by Christian Feuers anger (author of pgfplots). It has been contributed to Tik Z as general purpose library, so the reference documentation along with all tweaks can be found in [5, Section Externalization Library]. The command \usepgfplotslibrary{external} is actually just a wrapper which loads \usetikzlibrary{external} or, if this library does not yet exist because the installed pgf has at most version 2.00, it will load a copy which is shipped with pgfplots.

A library which allows the user to typeset several plots in a matrix like structure. Often one has to compare two plots to one another, or you simply need to display two plots in conjunction with each other. Either way the following section describes this library which makes matrix structure easier than alternative methods discussed in Section 4.19.4. \begin{groupplot}[ options ] environment contents \end{groupplot} Once you have loaded the groupplots library you will gain access to this environment. This environment is limited to the same restrictions as the axis environment. It actually utilizes this environment so consider it as an extension of this. What is important to note is that [ options ] are applied to all plots in the entire environment. This can be really handy when you need the same xmin, xmax, ymin and ymax. With such an environment one can typeset plots in matrix like styles 2 1 0 0 2 1.5 1 0 1 2 1 2 2 1 0 0 0.5 1 2 1 0 0 1 2 2 1.5 1 0 1 2 2 1 0 0 1 2 2 1 0 0 0.5 1 2 1 0 0 1 2

The equivalent code is seen as the second example and it is clear that you have to type a lot less. So how do you use it? First of all you need to utilize the new environment groupplot. Within this environment the following command works.

/pgfplots/group style={ options with group/ prex } This key sets all options using the /pgfplots/group/ prex. Note that the distinction between group/ and normal options is important as some of them are quite similar. For example, the following statements are all equivalent:\pgfplotsset{group style={a=2,b=3}} \pgfplotsset{group/a=2,group/b=3} \pgfplotsset{group/.cd,a=2,b=3}

All the following keys are in the subdirectory group. /pgfplots/group/group size= columns by rows /pgfplots/group/columns= columns /pgfplots/group/rows= rows (initially 1 by 1) (initially 1) (initially 1)

These keys determine the total number of plots that can be in one environment groupplot. It is thus important not to add more \nextgroupplot in the environment than columns rows . This is critical to set if one uses more than 1 more plot. As the key group size uses columns and rows you should stick to either group size or both columns and rows. /pgfplots/group/horizontal sep= dimension /pgfplots/group/vertical sep= dimension (initially 1cm) (initially 1cm)

The spacing between the plots in the horizontal and vertical direction, respectively. If you thus want them to be glued together you should set them both to a length of 0pt. /pgfplots/group/every plot/.style={ style } (initially empty)

This style is used on every plot as the rst style. It is thus equivalent as options in the groupplot environment. /pgfplots/group/xlabels at=all|edge bottom|edge top /pgfplots/group/ylabels at=all|edge left|edge right (initially all) (initially all)

In order to determine which plots get labels typeset one can use these keys. By default all axes get typeset normally and thus have both x and y axis labels.

2 1 .5 1 0 .5 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2

c / mol/L

1 .5 1 0 .5 0

(2,1)}; (2,1)}; (2,1)}; (2,1)};

time t / h

time t / h

In the example above, only the bottom row gets the label dened in the beginning groupplotenvironment on the x axis and only the rst column of plots gets labels on the y axis on their left side. These keys are especially handy when using glued plots. /pgfplots/group/xticklabels at=all|edge top|edge bottom /pgfplots/group/yticklabels at=all|edge left|edge right (initially all) (initially all)

In order to determine which plots get tick labels typeset one can use these keys. By default all axes gets typeset normally and thus have both x and y axis tick labels. If one sets\pgfplotsset{group/xticklabels at=edge bottom,group/yticklabels at=edge right}

only the bottom row gets tick labels on the x axis and only the last column gets tick labels on the y axis on their right side. These keys are specially handy when using glued plots. Keep in mind that this is implies the same ticks for all plots. /pgfplots/group/x descriptions at=all|edge top|edge bottom /pgfplots/group/y descriptions at=all|edge left|edge right (initially all) (initially all)

These are simply a short hand for using both xticklabels at and xlabels at simultaneously:

(1,2) (2,1)}; (1,2) (2,1)}; (1,2) (2,1)}; (1,2) (2,1)};

Here, x descriptions at=edge bottom yields that x descriptions (xlabel and xticklabel) are only used for the lowest row. Furthermore, y descriptions at=edge right places y descriptions only for the rightmost column. Consider modifying the horizontal sep and vertical sep for your needs. As for xticklabels at, usage of this key implies the same ticks for all plots. This might require compat=1.3 (or newer). /pgfplots/group/group name={ name } (initially group)

/pgfplots/group/empty plot/.style={ style }

(initially /pgfplots/hide axis)

This key can be used as an option to the command \nextgroupplot. This makes the next plot invisible (only the axes) but maintains it anchors and name. If you want it to behave in another style then you can redene it. Consider the same example as before.

A patch plot is a plot in which each individual patch is available. Here, available means that the user provided each individual patch manually. This can be achieved by means of a long series of patches which have been concatenated in a suitable way (compare the description of patch plots in section 4.6.12) or by means of a mathematical expression which is sampled (compare the key patch type sampling). Most patch types expect a series of point evaluations in a specic sequence. Note that even though each individual patch might have a smooth boundary, the patchplots library does not interpolate smoothly between adjacent patches. Consequently, it is task of the one who creates the patches (which means: evaluated some function at its vertices) to ensure that patches can be glued together in an adequate way. This allows a lot of freedom, including both jumps and smoothly concatenated edges. The patchplots library comes with a couple of inherently twodimensional patch types (including second order triangles/rectangular patches and cubic tensor product patches known for nite elements). Typically, these patches live in a threedimensional axis. Often, they are used to visualize the surface of function values f (x, y ). The patchplots library ensures that such patches are drawn in a way which respects the current view. In particular, if a patch folds over itsself (which is possible), it is drawn such that foreground areas are in the foreground and background areas are in the background. The patchplots library comes with smoothly shaded patches. More precisely, both the boundary of patches and their color shading are smooth. Note, however, that the patch boundary typically has much more smoothness than the color shading. The patchplots library also allows automatic conversion from a higherorder patch to triangles (triangulation) by means of the key patch to triangles. Furthermore, it features automatic patch refines. Use the patchplots library if you want to have smooth boundaries for your patches, or if you need advanced shadings, or if you want polygon plots, or if you want more freedom in onedimensional patches.

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5.6.1

Additional Patch Types

/pgfplots/patch type=default|rectangle|triangle|line|quadratic spline|cubic spline| bilinear|triangle quadr|biquadratic|bicubic|polygon|coons|tensor bezier (initially default) The patchplots library supports several new patch types in addition to the initially available choices (which are rectangle,triangle and line). The documentation of the twodimensional choices from page 154 is repeated here. The new patch types are discussed in detail on the following pages. OneDimensional Patch Types There are two new onedimensional patch types, namely quadratic spline and cubic spline. Here, patch type=quadratic spline consists of quadratic patches of n = 3 vertices each. The vertices are interpolated exactly: patch type=quadratic spline 2 (5)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

In our example, the rst segment interpolates f (x) = x2 at the points {0, 1/2, 1}. The quadratic spline is actually nothing but piecewise Lagrangian interpolation with quadratic polynomials: it expects three points in the sequence (left end), (right end), (middle) and interpolates these three points with a quadratic polynomial. Unlike the default 1d mesh visualization (which uses patch type=line implicitly), you have to use the special syntax above (or the equivalent approach by means of patch table). Note that patch type=quadratic spline results in correct shapes, but uses just constant color for each segment; highorder color shading is only supported approximately using patch refines. The patch type=cubic spline is very similar: it expects patches of n = 4 vertices and interpolates them with a cubic polynomial: patch type=cubic spline 1 (1)% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, we interpolated f (x) = x3 at the four equidistant points {1, 1/3, 1/3, 1} with a cubic polynomial (which is x3 ). The cubic spline expects a sequence of patches, each with four coordinates, given in

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CHAPTER 5. RELATED LIBRARIES the sequence (left end), (right end), (interpolation point at 1/3), (interpolation point at 2/3). It has limitations and features like quadratic spline, see above. Providing Patches by means of Mathematical Expressions Most patch types expect a specic number of vertices in a specic sequence. This is part of what the patchplots library is. But is is still tedious to provide this sort of data. For simple patch types like line,rectangle and bilinear, you can provide the input coordinates with any of the input methods which are available for all other plot handlers. In particular, line is just a sharp plot (with individually colored segments) and rectangle is nothing but a surf plot. Note that both rectangle and bilinear also accept the standard matrix input (with scanlines, see mesh/ordering and its documentation). In summary: simple patch types accept a simple input format. /pgfplots/patch type sampling=true|false (initially false)

There are some complicated patch types. In particular, all patch types of higher order (i.e. quadratic spline, cubic spline, triangle quadr, biquadratic, bicubic) need more points than just their corners. For such patch types, you need to resort to mesh input=patches. That means you need to provide extra vertices and their function evaluation values in a specic sequence.

The patch type sampling method allows to simplify the procedure for such complicated patch types6 : it works together with \addplot expression and evaluates the mathematical expression at each of the required vertices (in the correct sequence): 1% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The rst plot above is almost a normal plot by expression. The samples and domain key controls the sampling procedure, and blue,point meta=none denes the global color to use. Note that the special choice point meta=none simply disables individual colors per mesh segment (which is the default for mesh plots). However, the patch type sampling key here makes a huge dierence: it tells pgfplots to check the current value of patch type and to sample a coordinate sequence which is suitable as input for that patch type. We see that the outcome is a partially smooth function (more about that below).6 Note

that patch type sampling is more or less useless for simple patch types.

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369

The method patch type sampling samples x just as usual. The result is a sequence [x0 , x1 , . . . , xk ]. For each interval [xi , xi+1 ], a patch type is sampled inside of the interval. To this end, the current patch type is used to generate a standardized vertex pattern in the unit cube. For patch type=cubic spline, this generates four points 0, 1/3, 2/3, 1. These standardized numbers are mapped into [xi , xi+1 ]. Then, any mathematical expressions (in our case exp(-x^2)) are evaluated at the resulting positions. The second plot in our example above shows the markers resulting from patch type sampling. Note that we see 13 markers even though we have said samples=5. These 5 samples are shown in the third plot. This is because patch type=cubic spline needs 4 points for each patch (i.e. 4 points in each sampled interval). Note that even though the result in our example above is partially smooth, it is not globally smooth. In other words: each resulting mesh segment is a polynomial of third order. But: the ve cubic polynomials are determined independently; and they are simple glued together without any intelligence. In particular, they are unsmooth at the ve initial sampling points! This key cannot apply global smoothing. It is really just a convenient method which simplies sampling of such patch types. The method patch type sampling can also be used for surf plots, i.e. for matrix sampling. It works in the same way:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example is similar to our onedimensional example above: it uses the same 1d function as product. We see that it has 132 samples instead of just 52 , and we see that the geometry is partially smooth (see above for partially). Note, however, that the color interpolation is only applied once per patch. The following example shows a bilinear patch with unsmooth geometry, but higher resolution for the color data, on a 13 13 mesh:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Note that you may want to view the preceding examples in Acrobat Reader. Many free pdf viewers cannot display these shadings properly.

370 Global OneDimensional Curves with Smooth Splines

CHAPTER 5. RELATED LIBRARIES

Typically, pgfplots assumes that you want individually colored patch segments whenever you use one of the plot handlers mesh, surf, or patch. The individual colors are determined by the current colormap and the value of point meta (compare section 4.8). Technically, individually colored path segments are one unit. If you fill them, you ll only one segment. You cannot ll them against the axis. In particular, you cannot use \closedcycle for individually colored mesh or patch plots. The patchplots library comes with onedimensional patch types like quadratic spline or cubic spline. It would be useful to draw a global path, that is: one which has a single color such that \closedcycle works. This is supported if you write point meta=none: Global path with cubic spline% Preamble: \pgfplotsset{width=7cm,compat=1.9}

} \closedcycle; \end{axis} \end{tikzpicture}

The use of point meta=none activates a special processing: the outcome is precisely one path. TwoDimensional Patch Types The patchplots library is especially strong for shader=interp, so this is our main focus in the remaining documentation here. Attention: At the time of this writing, many free pdf viewers do not fully support the following shadings7 . The preferred viewer is Adobe Acrobat Reader. The choice rectangle expects one or more rectangular patches with n = 4 vertices each. These vertices are either encoded as a matrix or as individual patches (using mesh input=patches), in the sequence in which you would connect the vertices:7 The author of this package has submitted bugxes to Linux viewers based on xpdf/libpoppler, so the problem will (hopefully) vanish in future versions.

As already documented on page 154, the shader=interp implementation for rectangle uses two triangles and interpolates them linearly. The dierences between the two examples above arise due to z buering approaches: the matrix input reorders the matrix in linear time, whereas the second example would sort complete rectangles. In our case, this yields to the dierent corner sequence. The choice bilinear is essentially the same as rectangular with respect to its input formats and stroke paths, but it uses correct bilinear shading for shader=interp. Moreover, the geometry is also interpolated bilinearly instead of just two triangles. The two examples from above now become Bilinear from 2 2 matrix input (1) (2) 20 0 20 4 2 0 2 4 (3) 5 (0) 5 0% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Use patch type=bilinear if you want to improve the shape of individual patches and the quality of the color interpolation. In contrast to the simpler patch type=rectangle, it might result in a huger output document. The choice triangle expects a sequence of linear triangles, each encoded using n = 3 vertices: Single Triangle patch% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(0) (2) (5) (3) 0 (4) (1) 5 2 4 0

Here, the edges have the correct quadratic shape. However, the color interpolation is just bilinear ; using the color values of the corners and ignoring the rest (consider using patch refines to improve the color interpolation). For three dimensions, pgfplots checks the depth of corners to determine foreground/background. For two dimensions, strongly distorted elements may fold over each other in unexpected ways. The choice biquadratic expects a sequence of isoparametric biquadratic quadrilaterals each dened by n = 9 vertices. Their main use is to get rectangles with smooth boundaries: Single Biquadratic Quadrilateral 6 (6) (3) (8) (7) (5) (2)\addplot[patch,patch type=biquadratic, shader=interp,point meta=explicit] coordinates { (0,0) [1] (6,1) [2] (5,5) [3] (-1,5) [4] (3,1) [1] (6,3) [2] (2,6) [3] (0,3) [4] (3,3.75) [4] }; \end{axis} \end{tikzpicture}% Preamble: \pgfplotsset{width=7cm,compat=1.9}

(0) (3) (7) (4) 0 2 4 (6) (8) (1) 2 6 0 (2) (5) 4 6

Similar to triangle quadr, the edges have the correct quadratic shape but the color interpolation is just bilinear ; using the color values of the corners and ignoring the rest. Again, ensure that the mesh width is small enough in order to improve the quality of the color interpolation (see also patch refines).

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CHAPTER 5. RELATED LIBRARIES Note that a function of (x, y ) is biquadratic if it is quadratic w.r.t. x if y = const and also quadratic w.r.t. y if x = const (note that this is not an if and only if). For example, f (x, y ) = x2 y 2 is biquadratic. Consequently, we can represent a surface plot of f with just one biquadratic patch only the color interpolation is just bilinear. We do so using \addplot table[z expr= expression ]:% Preamble: \pgfplotsset{width=7cm,compat=1.9}

We see that the shapes boundary is reconstructed exactly using the biquadratic patch. In addition, patch refines improves the (rst order) color interpolation. Details for patch refines are discussed in Section 5.6.2 and details and limitations regarding superimposed grid lines are discussed in Section 5.6.4. Note that biquadratic can easily be combined with patch type sampling in order to sample an arbitrary surface plot with smooth boundaries. A patch with type biquadratic and shader=interp has a bounding box which is determined from the input vertices. Due to the high order of the patch, parts of the patch can be outside of that bounding box. This holds for all advanced patch types. The choice bicubic is similar to biquadratic: it allows to denes twodimensional patches whose boundary is dened by four cubic polynomials. Consequently, it allows very smooth boundaries especially since the viewer constructs these boundaries at every zoom level. A bicubic patch is constructed from 16 points which are arranged in a 4 4 matrix. Each consecutive 16 points make up a single bicubic patch. The 17th point starts the next bicubic patch (just as for any other patch type). Single Bicubic Quadrilateral% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Just as for biquadratic, the color interpolation of bicubic is (just) bilinear, even though the geometry is of higher order. The color interpolation uses the point meta values determined at the four corners of each patch; all other values of point meta are ignored by the shader (although their values are used to compute point meta min and point meta max).

The previous example uses two patches of type bicubic. Note that the color data (point meta) has been provided explicitly and its values are only used at the corners (the [1] value after the point (4,1,.5) is ignored). Color interpolation of bicubic patches uses only the color data at the patchs corners. The remaining color data values are ignored. Note that if you leave the default (which is point meta=f(x) instead of point meta=explicit), the second patch will be blue. This is because the four corner vertices of the second patch dene the color shading and their z value is 0. Note that bicubic can easily be combined with patch type sampling in order to sample an arbitrary surface plot with smooth boundaries. Just as described for biquadratic, a patch with type bicubic and shader=interp can have a bounding box which is slightly smaller than the region which is actually drawn (because the bounding box is computed from the input points). The choice coons expects a sequence of one or more Coons patches, made up of n = 12 points each. A Coons patch is delimited by four cubic B ezier curves, with the end points attached to each other and the n points provide the required control points for these curves in a specic ordering which is illustrated in the following example: A Coons Patch 4 3 2 1 0 1 2 3 (11) (10) (0) (8) (1) (9) (3) (5) (6) (2) (7) (4)

376% Preamble: \pgfplotsset{width=7cm,compat=1.9}

CHAPTER 5. RELATED LIBRARIES

\begin{tikzpicture} \begin{axis}[nodes near coords={(\coordindex)}, width=12cm, title=A Coons Patch] \addplot[mark=*,patch,patch type=coons, shader=interp,point meta=explicit] coordinates { (0,0) [0] % first corner (1,-1) [0] % Bezier control point between (0) and (3) (4,0.7) [0] % Bezier control point between (0) and (3) % (3,2) [1] % second corner (4,3.5) [1] % Bezier control point between (3) and (6) (7,2) [1] % Bezier control point between (3) and (6) % (7,1) [2] % third corner (6,0.6) [2] % Bezier control point between (6) and (9) (4.5,-0.5) [2] % Bezier control point between (6) and (9) % (5,-2) [3] % fourth corner (4,-2.5) [3] % Bezier control point between (9) and (0) (-1,-2) [3] % Bezier control point between (9) and (0) }; \end{axis} \end{tikzpicture}

The four cubic B ezier curves are equivalent to curveto paths of pgf, i.e. to a sequence of the form ( corner 1 ).. controls( control point A ) and ( control point B ) .. ( corner 2 ). The interpolated shading is bilinear. More precisely, a bilinear shading in the unit cube [0, 1]2 is initialised which is then mapped into the Coons patch such that the corners match. The color interpolation uses only the color data of the four corners, color values of intermediate control points are ignored for the shading (although their value will be respected for the upper and lower limit of color data). In contrast to the nite element patches, a Coons patch is inherently twodimensional. While you can still use three dimensional coordinates, pgfplots will draw the shading as you provide it, without checking for the depth information (as it does for the other patch types). In other words: depending on the current view angle, the shading might fold over itself in unexpected ways. Even for two dimensions, Coons patches may fold over themselves. To determine which part is foreground and which part is background, the following rule applies: the four corner points (0), (3), (6), (9) are associated to the unit cube points (u, v ) = (0, 0), (0, 1), (1, 1) and (1, 0), respectively. The edge between corner (3) and (6) (i.e. the one with v = 1) is foreground, the edge between (1) and (9) is background. Thus, large values of v are drawn on top of small values of v . If v is constant, large values of u are drawn on top of small values of u. Thus, reordering the patch vertices (choosing a dierent rst vertex and/or reversing the sequence) allows to get dierent foreground/background congurations8 . Note that patch type sampling is unavailable for patch type=coons because the control points are no point evaluation of the same function. The choice tensor bezier is similar to patch type=coons: it allows to dene a bezier patch. However, it allows more freedom: it has 16 control points instead of the 12 of a coons patch. The four additional control points are situated in the center of each patch. This patch type generates .pdf shadings of type 7 (whereas coons patches are shadings of type 6). It has been added for reasons of completeness, although it has not been tested properly. Please refer to the specication of the .pdf format for details9 . The choice tensor bezier is actually the same as patch type=bicubic except that bicubic automatically respects the view depth (foreground/background) and is given in a dierent by means of function evaluations rather than control points. Note that patch type sampling is unavailable for patch type=tensor bezier because the control points are no point evaluation of the same function. The choice polygon expects polygons with a xed number of vertices. This patch type requires the number of vertices as argument: /pgfplots/vertex count= count8 Internally, pgfplots employs such mechanisms to map the higher order isoparametric patch types to Coons patches, sorting according their corners depth information. 9 If someone is willing to test it and document it, feel free to email me!

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The number of vertices to be used for patch type=polygon. The number can be arbitrary. All input patches are expected to have this many vertices but it is acceptable if a patch uses the same vertex multiple times. This means that patch type=polygon accepts polygons with dierent numbers of vertices, but you need to apply some sort of manual padding. This parameter is (currently) mandatory. A patch plot with patch type=polygon simply connects the n=vertex count vertices in their order of appearance and closes the resulting path: 3 4 7 0 6 0 0 1 y 0 1 2 2 1 x 2% Preamble: \pgfplotsset{width=7cm,compat=1.9}

The example above denes the patch by means of a connectivity table (patch table with point meta) and a vertex list (the normal input coordinates of the plot): there are 8 vertices and 4 polygons. Note that 2 of these polygons are triangles, one has 4 corners and only of them actually has all 5 allocated corners. This eect can be achieved by replicating one of the corners. The connectivity table in our example denes a unique color for each polygon: 0 for the rst patch, 1 for the second, 2 for the third, and 3 for the last. These numbers map into the current colormap. The patch type=polygon supports neither triangulation nor shading nor renement. The order of appearance of the input points is supposed to be the order in which the lineto operations of the resulting path are generated.

5.6.2

Automatic Patch Renement and Triangulation

pgfplots supports automatic patch renement for most of its patch types. There are mainly two purposes for patch renement: to increase the quality of z buffer=sort and/or to improve color interpolation for highorder patches. /pgfplots/patch refines={ levels } (initially 0)

This key controls patch renement. The initial choice patch refines=0 disables renement and visualizes elements as they have been found in input les. A positive levels enables (recursive) patch renement: each patch is rened individually.

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CHAPTER 5. RELATED LIBRARIES The following example illustrates the patch refines feature for a triangle quadr shape function on an edge. Note that since pgfplots uses only rst order shading which is based on the corner points (0), (1) and (2), the specied shape function of patch refines=0 has constant color. Higher levels approximate the patch with increasing quality:patch renes=0 patch renes=1 patch renes=2

In this example, patch renement makes a huge dierence since it is just one element with huge displacements. For practical examples, you probably wont need many renement levels. The rened patches reproduce the geometrys shape exactly. In addition, they improve color interpolation. Note that its purpose is just visualization, therefor hanging nodes are allowed (and will be generated by patch refine for most patch types). Patch renement is implemented for all supported patches except for patch type=coons, tensor bezier, bicubic (might follow eventually) and polygon. /pgfplots/patch to triangles=true|false (initially false)

Occasionally, one has a complicated patch type on input and would like to visualize it as a triangle mesh. pgfplots supports automatic triangulation of patches. Triangulation means to replace each individual input patch by one or more triangles. Triangulation can be combined with patch refines in which case patch refines is applied rst and the resulting rened patches are then triangulated.Triangulation + 0 renes Triangulation + 1 renes Triangulation + 2 renes

For onedimensional patch types like quadratic spline, patch to triangles results in approximation by means of patch type=line instead of triangle. The patch to triangles feature is implemented for all supported patches except for patch type=coons, tensor bezier, and polygon.

5.6.3

Peculiarities of Flat Shading and High Order Patches

The patchplots library has been optimized for use with interpolated shadings, i.e. for shader=interp: it allows the lled area to fold over itself or to be outside of the patch boundaries. pgfplots also supports shader=flat and shader=faceted by simply stroking and/or lling the patch boundaries. Naturally, such an approach works only if the enclosed patch boundary and the lled area are essentially the same! Consider using shader=flat or shader=faceted only if the mesh width is small enough such that patches do not fold over themselves. The following example illustrates the eect: the coarse single element on the left folds over itsself, resulting in strange ll patterns. Rening the mesh reduces the eect.Faceted + 0 renes Faceted + 1 renes Faceted + 2 renes

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5.6.4

Drawing Grids

The patchplots library supports grid (mesh) visualization in the same way as for two/threedimensional mesh- and surf plots. This includes four dierent approaches: the rst is shader=faceted, which uses constant ll color and faceted color for stroke paths (as we already saw in Section 5.6.3). The second approach is to use shader=faceted interp which uses interpolated shadings for lling and issues stroke paths on top of each interpolated element. The third approach is to issue two \addplot commands, one with the lled patch plot, and one with a patch,mesh style which only draws (colored) grid lines on top of the previous plot. The three approaches are shown below. Grids with shader=faceted% Preamble: \pgfplotsset{width=7cm,compat=1.9}

As already discussed in Section 5.6.3, the approach with shader=faceted works well if the mesh width is small enough (such that single patches do not overlap and their ll area is within the patch boundaries). Grids with shader=faceted interp% Preamble: \pgfplotsset{width=7cm,compat=1.9}

Here, grid lines are dened to be the patch boundary, so it may occasionally happen for coarse patches that grid lines cross the lled area. If you experience problems, consider using the patch refines key. The shader=faceted interp supports z buffer at the cost of generating one shading for each patch element (the stroke path is drawn immediately after the patch element is shaded). This can become quite expensive10 at display time and may lead to huge pdf les. However, shader=faceted interp provides smooth shadings and, at the same time, good grid lines which are drawn in the correct order.10 I

would really like to hear any wellfounded ideas how to improve this issue. In case you have an idea let me know!

The approach to draw grids separately is done by means of two \addplot statements; the rst using patch as before, the second using patch,mesh. This congures pgfplots to visualize just the mesh. Make sure you provide mesh after patch since the latter activates lled surf visualization. The approach of meshes on top of patches implies to draw grid lines simply over any previous drawing operations. Thus, depth information is lost (as displayed in the rst example above). Overlaying grid lines on top of the surface works in special cases (see bottom picture). An approach which always works is to provide the mesh at a xed z position as displayed in the following example:

Here, the rst \addplot3 command is the same as above, just with shader=interp. The second reproduces the same geometry, but uses a z filter to x the z coordinate (in this case to z = 1.8). This eectively overrules all z coordinates. Thus, grid lines can be drawn either by means of at ll color with shader=faceted (ecient), by means of interpolated ll colors with shader=faceted interp (inecient, see above) or, for special applications, using a separate patch,mesh plot which is drawn on top of the patches (ecient). In any case, the mesh visualization considers the faceted color which can depend on mapped color.

\begin{polaraxis} environment contents \end{polaraxis} The polar library provides the polaraxis environment. Inside of such an environment, all coordinates are expected to be given in polar representation of the form ( angle , radius ), i.e. the x coordinate is always the angle and the y coordinate the radius:

Furthermore, you can use all of the supported input coordinate methods (like \addplot coordinates, \addplot table, \addplot expression). The only dierence is that polar axes interpret the (rst two) input coordinates as polar coordinates of the form ( angle in degrees , radius ). It is also possible to provide \addplot3; in this case, the third coordinate will be ignored (although it can be used as color data using point meta=z). An example can be found below in Section 5.7.3.

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The data cs key is described in all detail on page 329; it tells pgfplots the coordinate system of input data. pgfplots will then take steps to automatically transform each coordinate into the required coordinate

5.7. POLAR AXES system (in our case, this is data cs=polar).

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5.7.3

Mixing With Cartesian Coordinates

Similarly to the procedure described above, you can also provide Cartesian coordinates inside of a polar axis: simply tell pgfplots that it should automatically transform them to polar representation by means of data cs=cart: Cartesian Input 120 150 90 60 30% Preamble: \pgfplotsset{width=7cm,compat=1.9}

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More details about the data cs key can be found on page 329. This does also allow more involved visualization techniques which may operate on Cartesian coordinates. The following example uses \addplot3 to sample a function f : R2 R, computes contour lines (with the help of gnuplot) and displays the result in a polaraxis: 120 1500. 2

What happens is that z = exp(x2 y 2 ) is sampled for x, y [3, 3], then contour lines are computed on (x, y, z ), then the resulting triples (x, y, z ) are transformed to polar coordinates (, r, z ) (leaving z intact). Finally, the z coordinate is used as point meta to determine the color. Note that \addplot3 allows to process threedimensional input types, but the result will always be two dimensional (the z coordinate is ignored for point placement in polaraxis). However, the z coordinate can be used to determine point colors (using point meta=z).

5.7.4

Special Polar Plot Types

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/tikz/polar comb \addplot+[polar comb]

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CHAPTER 5. RELATED LIBRARIES The polar comb plot handler is provided by Tik Z; it draws paths from the origin to the designated position and places marks at the positions (similar to the comb plot handler). Since the paths always start at the origin, it is particularly suited for polaraxis: 120 150 90% Preamble: \pgfplotsset{width=7cm,compat=1.9}

using complex number division. The result is always in the unit circle. The main application for Smith Charts is in the area of electrical and electronics engineers specializing in radio frequency: to show the reection coecient r(z ) for normalised impedance z . It is beyond the scope of this manual to delve into the radio frequency techniques; for us, it is important to note that the smithchart library supports the data map r(z ) shown above, an axis class which interprets x as the real components and y as the imaginary components, a visualization of grid lines as arcs, the possibility to stop grid lines to allow uniform spacing in Smith Charts, a large set of the pgfplots axis ne tuning parameters, input of already mapped coordinates r(z ) (i.e. Cartesian coordinates in the unit circle), many of the pgfplots plot handlers.

5.8.1

Smith Chart Axes

\begin{smithchart}[ options ] environment contents \end{smithchart} The \begin{smithchart} environment draws Smith Charts. It accepts the same options \begin{axis}. In fact, it is equivalent to \begin{axis}[ options ,axis type=smithchart]. as

5.8. SMITH CHARTS Impedance Smith Chart 1 0.5 2

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The example above visualizes three data points using the initial conguration of Smith Charts; the data points are interpreted as complex numbers z = x + jy and are mapped using r(z ). Here, the x coordinate refers to the cycles described by the horizontal line whereas the y coordinate refers to the cycles described by the tick labels on the outside. /pgfplots/smithchart mirrored=true|false (initially false)

Since such a chart easily becomes crowded, it should be tuned manually by means of suitable appearance options (if you feel that there is a suitable default, let me know). Details for show origin, yticklabel around circle, and yticklabel around circle* can be found later in this section.

5.8.2

Size Control

A Smith Chart can be resized by providing either width or height as argument to the axis. If you provide both, the Chart is drawn as an ellipsis. The tick and grid positions for smithchart axes are realized by means of three manually tuned sets of grid lines: one for small-sized plots, one for medium-sized plots and one for huge plots. The actual parameters for width or height are considered to select one of the following sets: /pgfplots/few smithchart ticks (style, no value)

Note that few smithchart ticks contains syntactical overhead to distinguish between default ticks and nal tick positions: it does not assign xtick and ytick directly. Instead, it provides them as separate default xtick style arguments. The purpose of this distinction is to mark them as default arguments the underlying styles smithchart/every default xtick is used if and only if there is no xtick value given. In case you want to override this default, you can either copypaste the denition above and adjust it or omit all the default smithchart xtick/.style stu and write xtick={ your list } directly.

As mentioned, the only purpose of the default smithchart xtick/.style overhead is to distinguish between \begin{smithchart}[xtick={ user dened }] and default arguments (see the documentation of default smithchart xtick/.style for more about this technical detail). For ne tuning of the scaling decisions, see the smith chart ticks by size key. /pgfplots/many smithchart ticks (style, no value)

The many smithchart ticks style is used for every Smith Chart whose width exceeds 14cm although it is less than 20cm:

We see that many smithchart ticks has dierent placement and alignment options than few smithchart ticks: it uses sloped tick labels inside of the unit circle for the y descriptions (imaginary axis). The initial conguration is realized by means of two separate styles: one which denes only the tick positions (the many smithchart ticks* style) and one which also changes placement and alignment options. The initial conguration can be changed individually (see the end of this section for examples). The initial conguration is:

Attention: This style might change in future versions! Similarly to many smithchart ticks (see above), the initial conguration is realized by means of two separate styles: one which denes only the tick positions (the many smithchart ticks* style) and one which also changes placement- and alignment options: